path: root/monte-carlo.bib

@article{jose_renormalization_1977,
	title = {Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model},
	volume = {16},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.16.1217},
	doi = {10.1103/PhysRevB.16.1217},
	abstract = {The classical planar Heisenberg model is studied at low temperatures by means of renormalization theory and a series of exact transformations. A numerical study of the Migdal recursion relation suggests that models with short-range isotropic interactions rapidly become equivalent to a simplified model system proposed by Villain. A series of exact transformations then allows us to treat the Villain model analytically at low temperatures. To lowest order in a parameter which becomes exponentially small with decreasing temperature, we reproduce results obtained previously by Kosterlitz. We also examine the effect of symmetry-breaking crystalline fields on the isotropic planar model. A numerical study of the Migdal recursion scheme suggests that these fields (which must occur in real quasi-two-dimensional crystals) are strongly relevant variables, leading to critical behavior distinct from that found for the planar model. However, a more exact low-temperature treatment of the Villain model shows that hexagonal crystalline fields eventually become irrelevant at temperatures below the Tc of the isotropic model. Isotropic planar critical behavior should be experimentally accessible in this case. Nonuniversal behavior may result if cubic crystalline fields dominate the symmetry breaking. Interesting duality transformations, which aid in the analysis of symmetry-breaking fields are also discussed.},
	number = {3},
	urldate = {2018-04-04},
	journal = {Physical Review B},
	author = {José, Jorge V. and Kadanoff, Leo P. and Kirkpatrick, Scott and Nelson, David R.},
	month = aug,
	year = {1977},
	pages = {1217--1241},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/RMHXAR3A/PhysRevB.16.html:text/html;José et al. - 1977 - Renormalization, vortices, and symmetry-breaking p.pdf:/home/pants/.zotero/data/storage/M2V99JHC/José et al. - 1977 - Renormalization, vortices, and symmetry-breaking p.pdf:application/pdf}
}

@article{wu_potts_1982,
	title = {The {Potts} model},
	volume = {54},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.54.235},
	doi = {10.1103/RevModPhys.54.235},
	abstract = {This is a tutorial review on the Potts model aimed at bringing out in an organized fashion the essential and important properties of the standard Potts model. Emphasis is placed on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective. Topics reviewed include the mean-field theory, duality relations, series expansions, critical properties, experimental realizations, and the relationship of the Potts model with other lattice-statistical problems.},
	number = {1},
	urldate = {2018-04-04},
	journal = {Reviews of Modern Physics},
	author = {Wu, F. Y.},
	month = jan,
	year = {1982},
	pages = {235--268},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/TJ83QK5V/RevModPhys.54.html:text/html;Wu - 1982 - The Potts model.pdf:/home/pants/.zotero/data/storage/KN9S57Z9/Wu - 1982 - The Potts model.pdf:application/pdf}
}

@article{coniglio_exact_1989,
	title = {Exact relations between droplets and thermal fluctuations in external field},
	volume = {22},
	issn = {0305-4470},
	url = {http://stacks.iop.org/0305-4470/22/i=17/a=006},
	doi = {10.1088/0305-4470/22/17/006},
	abstract = {The authors extend the definition of droplets in Ising and Potts models to the case of an external field different from zero. They also find exact relations between thermal properties and connectivity properties which show why, in mean field, the mean cluster size does not diverge as the susceptibility when the critical temperature is approached from below.},
	language = {en},
	number = {17},
	urldate = {2018-04-04},
	journal = {Journal of Physics A: Mathematical and General},
	author = {Coniglio, A. and Liberto, F. de and Monroy, G. and Peruggi, F.},
	year = {1989},
	keywords = {cluster-algorithm},
	pages = {L837},
	file = {IOP Full Text PDF:/home/pants/.zotero/data/storage/2MABVQ35/Coniglio et al. - 1989 - Exact relations between droplets and thermal fluct.pdf:application/pdf}
}

@article{wolff_comparison_1989,
	title = {Comparison between cluster {Monte} {Carlo} algorithms in the {Ising} model},
	volume = {228},
	issn = {0370-2693},
	url = {http://www.sciencedirect.com/science/article/pii/0370269389915633},
	doi = {10.1016/0370-2693(89)91563-3},
	abstract = {We report autocorrelation times for the Swendsen-Wang algorithm and for a recently proposed single cluster variant in the 2D and 3D Ising models at criticality. The new algorithm decorrelates faster in all cases and gains about an order of magnitude on a 643 lattice. Critical slowing down is practically negligible and possibly completely absent in three dimensions. Results on static properties of the 3D model are consistent with published data.},
	number = {3},
	urldate = {2018-04-04},
	journal = {Physics Letters B},
	author = {Wolff, Ulli},
	month = sep,
	year = {1989},
	pages = {379--382},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/F8LMC2TH/Wolff - 1989 - Comparison between cluster Monte Carlo algorithms .pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/I8GWCEUL/0370269389915633.html:text/html}
}

@article{alexandrowicz_swendsen-wang_1989,
	title = {Swendsen-{Wang} simulation of {Ising} spins and a precise definition of critical clusters},
	volume = {160},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/0378437189904457},
	doi = {10.1016/0378-4371(89)90445-7},
	abstract = {A recent ultrafast simulation of Ising spins (σi = ± 1) utilizes a random + to − flip-over of duly defined decoupled blocks of spins. We show that the random dynamics alone suffices to prove the correspondence of the blocks with “critical clusters” describing thermal (magnetic) fluctuation. (The precise requirement is σiσi = 1, for a pair of spins inside a block, and 〈σiσj〉 = 0, for a σi inside and σj, outside.) The present approach helps to extend the study of critical clusters, and also ultrafast simulation, to the case of nonzero magnetization. Finite critical clusters constitute always a ± symmetric set and are very different (much smaller) than continuous domains of similarly oriented spins.},
	number = {3},
	urldate = {2018-04-04},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Alexandrowicz, Z.},
	month = oct,
	year = {1989},
	pages = {310--320},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/TCTPEINC/Alexandrowicz - 1989 - Swendsen-Wang simulation of Ising spins and a prec.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/ZYI82U3R/0378437189904457.html:text/html}
}

@article{wolff_collective_1989,
	title = {Collective {Monte} {Carlo} {Updating} for {Spin} {Systems}},
	volume = {62},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.361},
	doi = {10.1103/PhysRevLett.62.361},
	abstract = {A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality. We demonstrate its efficiency in the two-dimensional O(n) σ models for n=1 (Ising) and n=2 (x−y) at their critical temperatures, and for n=3 (Heisenberg) with correlation lengths around 10 and 20. On lattices up to 1282 no sign of critical slowing down is visible with autocorrelation times of 1-2 steps per spin for estimators of long-range quantities.},
	number = {4},
	urldate = {2018-04-04},
	journal = {Physical Review Letters},
	author = {Wolff, Ulli},
	month = jan,
	year = {1989},
	keywords = {monte-carlo, n-component, cluster-algorithm},
	pages = {361--364},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/P4IULUXD/PhysRevLett.62.html:text/html;Wolff - 1989 - Collective Monte Carlo Updating for Spin Systems.pdf:/home/pants/.zotero/data/storage/ANYNLLMY/Wolff - 1989 - Collective Monte Carlo Updating for Spin Systems.pdf:application/pdf}
}

@article{destri_swendsen-wang_1992,
	title = {Swendsen-{Wang} {Monte} {Carlo} study of the {Ising} model with external field},
	volume = {278},
	issn = {0370-2693},
	url = {http://www.sciencedirect.com/science/article/pii/037026939290199E},
	doi = {10.1016/0370-2693(92)90199-E},
	abstract = {We present a Monte Carlo study of the scaling limit of the two-dimensional Ising model with external field. While no evidence is found for the E8 mass spectrum, we observe a very good agreement of our numerical data with the theoretical predictions for the magnetization and the correlation length.},
	number = {3},
	urldate = {2018-04-04},
	journal = {Physics Letters B},
	author = {Destri, C. and Di Renzo, F. and Onofri, E. and Rossi, P. and Tecchiolli, G. P.},
	month = mar,
	year = {1992},
	pages = {311--316},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/UWFALIWT/Destri et al. - 1992 - Swendsen-Wang Monte Carlo study of the Ising model.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/3GWTKW64/037026939290199E.html:text/html}
}

@article{lauwers_critical_1989,
	title = {The critical 2D {Ising} model in a magnetic field. {A} {Monte} {Carlo} study using a {Swendesen}-{Wang} algorithm},
	volume = {233},
	issn = {0370-2693},
	url = {http://www.sciencedirect.com/science/article/pii/0370269389906412},
	doi = {10.1016/0370-2693(89)90641-2},
	abstract = {We determine numerically the spin-spin correlation function in the scaling limit. These data are useful in order to check regularization procedures à la Dotsenko, based on conformal theory, of perturbation series expansions.},
	number = {1},
	urldate = {2018-04-04},
	journal = {Physics Letters B},
	author = {Lauwers, P. G. and Rittenberg, V.},
	month = dec,
	year = {1989},
	pages = {197--200},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/WBG7GBZA/Lauwers and Rittenberg - 1989 - The critical 2D Ising model in a magnetic field. A.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/I73J45VE/0370269389906412.html:text/html}
}

@article{ray_metastability_1990,
	title = {Metastability and nucleation in {Ising} models with {Swendsen}-{Wang} dynamics},
	volume = {167},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/037843719090276X},
	doi = {10.1016/0378-4371(90)90276-X},
	abstract = {The cluster numbers of stable phase droplets in the metastable state and nucleation rates for the three-dimensional Ising model with Swendsen-Wang dynamics are measured for T = 0.59 Tc and compared with previous Metropolis results. Both dynamics appear to give the same metastable properties. When the external field is small the results agree with classical nucleation theory. No evidence is found for the existence of a spinodal line.},
	number = {3},
	urldate = {2018-04-04},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Ray, T. S. and Wang, Jian-Sheng},
	month = sep,
	year = {1990},
	keywords = {monte-carlo, swendsen-wang, metastable, cluster-algorithm},
	pages = {580--588},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/HD9XTNQ3/Ray and Wang - 1990 - Metastability and nucleation in Ising models with .pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/L7RFGT7S/037843719090276X.html:text/html}
}

@article{wolff_critical_1990,
	title = {Critical slowing down},
	volume = {17},
	issn = {0920-5632},
	url = {http://www.sciencedirect.com/science/article/pii/092056329090224I},
	doi = {10.1016/0920-5632(90)90224-I},
	abstract = {The problem of critical slowing down in Monte Carlo simulations and some methods to alleviate or overcome it are reviewed: overrelaxation, multigrid and cluster algorithms.},
	urldate = {2018-04-04},
	journal = {Nuclear Physics B - Proceedings Supplements},
	author = {Wolff, Ulli},
	month = sep,
	year = {1990},
	pages = {93--102},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/DMY36YUQ/Wolff - 1990 - Critical slowing down.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/Y92EI3HC/092056329090224I.html:text/html}
}

@article{geyer_practical_1992,
	title = {Practical {Markov} {Chain} {Monte} {Carlo}},
	volume = {7},
	issn = {0883-4237},
	url = {http://www.jstor.org/stable/2246094},
	abstract = {Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature. In passing it touches on the Kipnis-Varadhan central limit theorem for reversible Markov chains, on some new variance estimators, on judging the relative efficiency of competing Monte Carlo schemes, on methods for constructing more rapidly mixing Markov chains and on diagnostics for Markov chain Monte Carlo.},
	number = {4},
	urldate = {2018-04-04},
	journal = {Statistical Science},
	author = {Geyer, Charles J.},
	year = {1992},
	pages = {473--483},
	file = {Geyer - 1992 - Practical Markov Chain Monte Carlo.pdf:/home/pants/.zotero/data/storage/UAU5QJNP/Geyer - 1992 - Practical Markov Chain Monte Carlo.pdf:application/pdf}
}

@article{el-showk_solving_2014,
	title = {Solving the 3d {Ising} {Model} with the {Conformal} {Bootstrap} {II}. \$\$\$\$-{Minimization} and {Preise} {Critial} {Exponents}},
	volume = {157},
	issn = {0022-4715, 1572-9613},
	url = {https://link.springer.com/article/10.1007/s10955-014-1042-7},
	doi = {10.1007/s10955-014-1042-7},
	abstract = {We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge {\textbackslash}(c{\textbackslash}) in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several {\textbackslash}({\textbackslash}mathbb \{Z\}\_2{\textbackslash})-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension {\textbackslash}({\textbackslash}Delta \_{\textbackslash}sigma = 0.518154(15){\textbackslash}), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.},
	language = {en},
	number = {4-5},
	urldate = {2018-04-04},
	journal = {Journal of Statistical Physics},
	author = {El-Showk, Sheer and Paulos, Miguel F. and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro},
	month = dec,
	year = {2014},
	pages = {869--914},
	file = {Full Text PDF:/home/pants/.zotero/data/storage/XB5EWQ28/El-Showk et al. - 2014 - Solving the 3d Ising Model with the Conformal Boot.pdf:application/pdf;Snapshot:/home/pants/.zotero/data/storage/9P7WJY86/s10955-014-1042-7.html:text/html}
}

@article{janke_nonlocal_1998,
	title = {Nonlocal {Monte} {Carlo} algorithms for statistical physics applications},
	volume = {47},
	issn = {0378-4754},
	url = {http://www.sciencedirect.com/science/article/pii/S0378475498001098},
	doi = {10.1016/S0378-4754(98)00109-8},
	abstract = {After a brief general overview of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications to phase transitions and critical phenomena. Here, standard simulations employing local update algorithms are severely hampered by the problem of critical slowing down, that is by strong correlations between successively generated data. It is shown that this problem can be greatly reduced by using nonlocal update techniques such as cluster and multigrid algorithms. The general ideas are illustrated for simple lattice spin models and Euclidean path integrals.},
	number = {2},
	urldate = {2018-04-05},
	journal = {Mathematics and Computers in Simulation},
	author = {Janke, Wolfhard},
	month = aug,
	year = {1998},
	keywords = {Critical phenomena, Cluster algorithms, Importance sampling, Monte Carlo simulations, Multigrid techniques, Phase transitions},
	pages = {329--346},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/N94BCGSZ/Janke - 1998 - Nonlocal Monte Carlo algorithms for statistical ph.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/U22VXSJZ/S0378475498001098.html:text/html}
}

@article{coniglio_clusters_1980,
	title = {Clusters and {Ising} critical droplets: a renormalisation group approach},
	volume = {13},
	issn = {0305-4470},
	shorttitle = {Clusters and {Ising} critical droplets},
	url = {http://stacks.iop.org/0305-4470/13/i=8/a=025},
	doi = {10.1088/0305-4470/13/8/025},
	abstract = {The Migdal-Kadanoff renormalisation group for two-dimensions is employed to obtain the global phase diagram for the site-bond correlated percolation problem. It is found that the Ising critical point (K=K c, H=O) is a percolation point for a range of bond probability rho B such that 1{\textgreater}or= rho B {\textgreater}or=1-e -2 Kc . In particular, as rho B approaches 1-e -2 Kc , the percolation clusters become less compact and coincide with the Ising critical droplets.},
	language = {en},
	number = {8},
	urldate = {2018-04-05},
	journal = {Journal of Physics A: Mathematical and General},
	author = {Coniglio, A. and Klein, W.},
	year = {1980},
	pages = {2775},
	file = {IOP Full Text PDF:/home/pants/.zotero/data/storage/XH5C8THH/Coniglio and Klein - 1980 - Clusters and Ising critical droplets a renormalis.pdf:application/pdf}
}

@article{du_dynamic_2006,
	title = {Dynamic critical exponents for {Swendsen}–{Wang} and {Wolff} algorithms obtained by a nonequilibrium relaxation method},
	volume = {2006},
	issn = {1742-5468},
	url = {http://stacks.iop.org/1742-5468/2006/i=05/a=P05004},
	doi = {10.1088/1742-5468/2006/05/P05004},
	abstract = {Using a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen–Wang and Wolff algorithms. We examine dynamic relaxation processes following a quench from a disordered or an ordered initial state to the critical temperature T c , and measure the exponential relaxation time of the system energy. For the Swendsen–Wang algorithm with an ordered or a disordered initial state, and for the Wolff algorithm with an ordered initial state, the exponential relaxation time fits well to a logarithmic size dependence up to a lattice size L = 8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponent z exp = 1.19(2) up to L = 2048. For comparison, we also compute the effective dynamic exponents through the integrated correlation times. In addition, an exact result of the Swendsen–Wang dynamic spectrum of a one-dimensional Ising chain is derived.},
	language = {en},
	number = {05},
	urldate = {2018-04-05},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Du, Jianqing and Zheng, Bo and Wang, Jian-Sheng},
	year = {2006},
	pages = {P05004},
	file = {IOP Full Text PDF:/home/pants/.zotero/data/storage/NXZR9FP6/Du et al. - 2006 - Dynamic critical exponents for Swendsen–Wang and W.pdf:application/pdf}
}

@article{liu_dynamic_2014,
	title = {Dynamic scaling at classical phase transitions approached through nonequilibrium quenching},
	volume = {89},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.89.054307},
	doi = {10.1103/PhysRevB.89.054307},
	abstract = {We use Monte Carlo simulations to demonstrate generic scaling aspects of classical phase transitions approached through a quench (or annealing) protocol where the temperature changes as a function of time with velocity v. Using a generalized Kibble-Zurek ansatz, we demonstrate dynamic scaling for different types of stochastic dynamics (Metropolis, Swendsen-Wang, and Wolff) on Ising models in two and higher dimensions. We show that there are dual scaling functions governing the dynamic scaling, which together describe the scaling behavior in the entire velocity range v∈[0,∞). These functions have asymptotics corresponding to the adiabatic and diabatic limits, and close to these limits they are perturbative in v and 1/v, respectively. Away from their perturbative domains, both functions cross over into the same universal power-law scaling form governed by the static and dynamic critical exponents (as well as an exponent characterizing the quench protocol). As a by-product of the scaling studies, we obtain high-precision estimates of the dynamic exponent z for the two-dimensional Ising model subject to the three variants of Monte Carlo dynamics: for single-spin Metropolis updates zM=2.1767(5), for Swendsen-Wang multicluster updates zSW=0.297(3), and for Wolff single-cluster updates zW=0.30(2). For Wolff dynamics, we find an interesting behavior with a nonanalytic breakdown of the quasiadiabatic and diabatic scalings, instead of the generic smooth crossover described by a power law. We interpret this disconnect between the two scaling regimes as a dynamic phase transition of the Wolff algorithm, caused by an effective sudden loss of ergodicity at high velocity.},
	number = {5},
	urldate = {2018-04-05},
	journal = {Physical Review B},
	author = {Liu, Cheng-Wei and Polkovnikov, Anatoli and Sandvik, Anders W.},
	month = feb,
	year = {2014},
	pages = {054307},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/HUBB74C4/PhysRevB.89.html:text/html;Liu et al. - 2014 - Dynamic scaling at classical phase transitions app.pdf:/home/pants/.zotero/data/storage/C8PPDNT5/Liu et al. - 2014 - Dynamic scaling at classical phase transitions app.pdf:application/pdf}
}

@article{wang_cluster_1990,
	title = {Cluster {Monte} {Carlo} algorithms},
	volume = {167},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/037843719090275W},
	doi = {10.1016/0378-4371(90)90275-W},
	abstract = {The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example. Various generalizations are then reviewed and some applications are discussed. Two complete Fortran programs for the algorithms are provided.},
	number = {3},
	urldate = {2018-04-05},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Wang, Jian-Sheng and Swendsen, Robert H.},
	month = sep,
	year = {1990},
	pages = {565--579},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/K6Q27XAZ/Wang and Swendsen - 1990 - Cluster Monte Carlo algorithms.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/QTTQLTT3/037843719090275W.html:text/html}
}

@article{swendsen_nonuniversal_1987,
	title = {Nonuniversal critical dynamics in {Monte} {Carlo} simulations},
	volume = {58},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.58.86},
	doi = {10.1103/PhysRevLett.58.86},
	abstract = {A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order phase transitions, producing unusually small values of the dynamical critical exponent.},
	number = {2},
	urldate = {2018-04-05},
	journal = {Physical Review Letters},
	author = {Swendsen, Robert H. and Wang, Jian-Sheng},
	month = jan,
	year = {1987},
	pages = {86--88},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/V6CTHN82/PhysRevLett.58.html:text/html;Swendsen and Wang - 1987 - Nonuniversal critical dynamics in Monte Carlo simu.pdf:/home/pants/.zotero/data/storage/9H7NG55Z/Swendsen and Wang - 1987 - Nonuniversal critical dynamics in Monte Carlo simu.pdf:application/pdf}
}

@article{baillie_comparison_1991,
	title = {Comparison of cluster algorithms for two-dimensional {Potts} models},
	volume = {43},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.43.10617},
	doi = {10.1103/PhysRevB.43.10617},
	abstract = {We have measured the dynamical critical exponent z for the Swendsen-Wang and the Wolff cluster update algorithms, as well as a number of variants of these algorithms, for the q=2 and q=3 Potts models in two dimensions. We find that although the autocorrelation times differ considerably between algorithms, the critical exponents are the same. For q=2, we find that although the data are better fitted by a logarithmic increase in the autocorrelation time with lattice size, they are also consistent with a power law with exponent z≊0.25, especially if there are non-negligible corrections to scaling.},
	number = {13},
	urldate = {2018-04-05},
	journal = {Physical Review B},
	author = {Baillie, Clive F. and Coddington, Paul D.},
	month = may,
	year = {1991},
	pages = {10617--10621},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/UGDFYRN9/PhysRevB.43.html:text/html;Baillie and Coddington - 1991 - Comparison of cluster algorithms for two-dimension.pdf:/home/pants/.zotero/data/storage/QHJS4V7S/Baillie and Coddington - 1991 - Comparison of cluster algorithms for two-dimension.pdf:application/pdf}
}

@article{wang_clusters_1989,
	title = {Clusters in the three-dimensional {Ising} model with a magnetic field},
	volume = {161},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/0378437189904688},
	doi = {10.1016/0378-4371(89)90468-8},
	abstract = {We study the clusters generated in the Swendsen-Wang algorithm in a magnetic field. It is shown that the number of clusters is related to that of Coniglio and Klein by simple factors. With this definition of clusters, infinite size appears whenever the system has a nonzero magnetization. Scaling behavior of the number of clusters near the critical point is confirmed. The number of clusters away from the critical point for large cluster size s is consistent with ln n ≌ {\textbar}h{\textbar}s − Γ s2 3 on the low temperature side of the Coniglio-Klein cluster percolation transition line, and is consistent with ln n≌−({\textbar}h{\textbar} + c)s on the high temperature side. We also argue that this transition line is given by h = ±h̃(T)×(T-Tc)1 near Tc.},
	number = {2},
	urldate = {2018-04-05},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Wang, Jian-Sheng},
	month = nov,
	year = {1989},
	keywords = {ising},
	pages = {249--268},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/FQJTTTTH/Wang - 1989 - Clusters in the three-dimensional Ising model with.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/HRKDAKDL/0378437189904688.html:text/html}
}

@article{loos_symmetric_1969,
	title = {Symmetric spaces},
	author = {Loos, Ottmar},
	year = {1969},
	file = {Loos - 1969 - Symmetric spaces I.pdf:/home/pants/.zotero/data/storage/GX35WTRQ/Loos - 1969 - Symmetric spaces I.pdf:application/pdf;Loos - 1969 - Symmetric spaces II.pdf:/home/pants/.zotero/data/storage/AJFD39RN/Loos - 1969 - Symmetric spaces II.pdf:application/pdf}
}

@article{dimitrovic_finite-size_1991,
	title = {Finite-size effects, goldstone bosons and critical exponents in the d = 3 {Heisenberg} model},
	volume = {350},
	issn = {0550-3213},
	url = {http://www.sciencedirect.com/science/article/pii/055032139190167V},
	doi = {10.1016/0550-3213(91)90167-V},
	abstract = {The d = 3 classical O(3) Heisenberg model is studied numerically in the broken phase close to the critical point. The finite-size behaviour of the magnetisation and the correlation functions are shown to be in excellent agreement with the theoretical predictions obtained by chiral perturbation theory. The finite-size effects are governed by two constants, which are defined at infinite volume and zero magnetic field: the Goldstone boson decay constant F (or helicity modulus T = F2) and the magnetisation Σ. The data determine the scaling behaviour of Σ and F leading to the prediction 0.6930(2) for the critical coupling on simple cubic lattices and v′ = 0.73(4) and β = 0.36(2) for the correlation length and magnetisation critical indices, respectively.},
	number = {3},
	urldate = {2018-04-05},
	journal = {Nuclear Physics B},
	author = {Dimitrović, I. and Hasenfratz, P. and Nager, J. and Niedermayer, F.},
	month = feb,
	year = {1991},
	pages = {893--905},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/QD7P2N8S/Dimitrović et al. - 1991 - Finite-size effects, goldstone bosons and critical.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/H5G2N432/055032139190167V.html:text/html}
}

@article{chayes_graphical_1998,
	title = {Graphical {Representations} for {Ising} {Systems} in {External} {Fields}},
	volume = {93},
	issn = {0022-4715, 1572-9613},
	url = {https://link.springer.com/article/10.1023/B:JOSS.0000026726.43558.80},
	doi = {10.1023/B:JOSS.0000026726.43558.80},
	abstract = {A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state (Ashkin–Teller) model. Bonds in the graphical representation connect the Ashkin–Teller spins. For ferromagnetic systems it is proved that ordering is characterized by percolation in this representation. The representation leads immediately to cluster algorithms; some applications along these lines are discussed.},
	language = {en},
	number = {1-2},
	urldate = {2018-04-12},
	journal = {Journal of Statistical Physics},
	author = {Chayes, L. and Machta, J. and Redner, O.},
	month = oct,
	year = {1998},
	pages = {17--32},
	file = {Full Text PDF:/home/pants/.zotero/data/storage/JG5PWZTG/Chayes et al. - 1998 - Graphical Representations for Ising Systems in Ext.pdf:application/pdf;Snapshot:/home/pants/.zotero/data/storage/P9ILGDUH/BJOSS.0000026726.43558.html:text/html}
}

@article{machta_replica-exchange_2000,
	title = {Replica-exchange algorithm and results for the three-dimensional random field {Ising} model},
	volume = {62},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.62.8782},
	doi = {10.1103/PhysRevE.62.8782},
	abstract = {The random field Ising model with Gaussian disorder is studied using a different Monte Carlo algorithm. The algorithm combines the advantages of the replica-exchange method and the two-replica cluster method and is much more efficient than the Metropolis algorithm for some disorder realizations. Three-dimensional systems of size 243 are studied. Each realization of disorder is simulated at a value of temperature and uniform field that is adjusted to the phase-transition region for that disorder realization. Energy and magnetization distributions show large variations from one realization of disorder to another. For some realizations of disorder there are three well separated peaks in the magnetization distribution and two well separated peaks in the energy distribution suggesting a first-order transition.},
	number = {6},
	urldate = {2018-04-12},
	journal = {Physical Review E},
	author = {Machta, J. and Newman, M. E. J. and Chayes, L. B.},
	month = dec,
	year = {2000},
	pages = {8782--8789},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/UIKCMAUG/PhysRevE.62.html:text/html;Machta et al. - 2000 - Replica-exchange algorithm and results for the thr.pdf:/home/pants/.zotero/data/storage/6LTIQN3L/Machta et al. - 2000 - Replica-exchange algorithm and results for the thr.pdf:application/pdf}
}

@article{redner_graphical_1998,
	title = {Graphical representations and cluster algorithms for critical points with fields},
	volume = {58},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.58.2749},
	doi = {10.1103/PhysRevE.58.2749},
	abstract = {A two-replica graphical representation and associated cluster algorithm are described that are applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical representation. Results from numerical simulations of the Ising model in a staggered field are presented. For this case, the dynamic exponent for the algorithm is measured to be less than 0.5.},
	number = {3},
	urldate = {2018-04-12},
	journal = {Physical Review E},
	author = {Redner, O. and Machta, J. and Chayes, L. F.},
	month = sep,
	year = {1998},
	pages = {2749--2752},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/Q5RL6Q8U/PhysRevE.58.html:text/html;Redner et al. - 1998 - Graphical representations and cluster algorithms f.pdf:/home/pants/.zotero/data/storage/WYEU9G6Y/Redner et al. - 1998 - Graphical representations and cluster algorithms f.pdf:application/pdf}
}

@article{wolff_lattice_1988,
	title = {Lattice field theory as a percolation process},
	volume = {60},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.60.1461},
	doi = {10.1103/PhysRevLett.60.1461},
	abstract = {For a given lattice spin or gauge theory an associated correlated bond or plaquette percolation process is constructed. It is conjectured to reproduce the universal scaling behavior of the original model. Different field theories lead to different cluster weights generalizing a result by Fortuin and Kasteleyn for Potts models. The new representation lends itself to the design of Monte Carlo algorithms with reduced critical slowing down.},
	number = {15},
	urldate = {2018-04-17},
	journal = {Physical Review Letters},
	author = {Wolff, Ulli},
	month = apr,
	year = {1988},
	pages = {1461--1463},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/EFPZ9VED/PhysRevLett.60.html:text/html;Wolff - 1988 - Lattice field theory as a percolation process.pdf:/home/pants/.zotero/data/storage/EBMJTQ4T/Wolff - 1988 - Lattice field theory as a percolation process.pdf:application/pdf}
}

@article{guida_critical_1998,
	title = {Critical exponents of the {N} -vector model},
	volume = {31},
	issn = {0305-4470},
	url = {http://stacks.iop.org/0305-4470/31/i=40/a=006},
	doi = {10.1088/0305-4470/31/40/006},
	abstract = {Recently the series for two renormalization group functions (corresponding to the anomalous dimensions of the fields \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img1.gif] and \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img2.gif] ) of the three-dimensional \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img3.gif] field theory have been extended to next order (seven loops) by Murray and Nickel. We examine the influence of these additional terms on the estimates of critical exponents of the N -vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within the errors of the previous evaluation. Exponents such as \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img4.gif] (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou-Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img5.gif] expansions (order \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img6.gif] ), we have also re-analysed the determination of exponents from the \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img7.gif] -expansion. The conclusion is that the general agreement between \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img7.gif] -expansion and three-dimensional series has improved with respect to Le Guillou-Zinn-Justin.},
	language = {en},
	number = {40},
	urldate = {2018-04-18},
	journal = {Journal of Physics A: Mathematical and General},
	author = {Guida, R. and Zinn-Justin, J.},
	year = {1998},
	pages = {8103},
	file = {IOP Full Text PDF:/home/pants/.zotero/data/storage/K468APXL/Guida and Zinn-Justin - 1998 - Critical exponents of the N -vector model.pdf:application/pdf}
}

@article{fortuin_random-cluster_1972,
	title = {On the random-cluster model: {I}. {Introduction} and relation to other models},
	volume = {57},
	issn = {0031-8914},
	shorttitle = {On the random-cluster model},
	url = {http://www.sciencedirect.com/science/article/pii/0031891472900456},
	doi = {10.1016/0031-8914(72)90045-6},
	abstract = {The random-cluster model is defined as a model for phase transitions and other phenomena in lattice systems, or more generally in systems with a graph structure. The model is characterized by a (probability) measure on a graph and a real parameter κ. By specifying the value of κ to 1, 2, 3, 4, … is shown that the model covers the percolation model, the Ising model, the Ashkin-Teller-Potts model with 3, 4, … states per atom, respectively, and thereby, contains information on graph-colouring problems; in the limit κ ↓ 0 it describes linear resistance networks. It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.},
	number = {4},
	urldate = {2018-04-20},
	journal = {Physica},
	author = {Fortuin, C. M. and Kasteleyn, P. W.},
	month = feb,
	year = {1972},
	pages = {536--564},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/463W5CMX/Fortuin and Kasteleyn - 1972 - On the random-cluster model I. Introduction and r.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/EEHFQXUY/0031891472900456.html:text/html}
}

@article{stauffer_scaling_1979,
	title = {Scaling theory of percolation clusters},
	volume = {54},
	issn = {0370-1573},
	url = {http://www.sciencedirect.com/science/article/pii/0370157379900607},
	doi = {10.1016/0370-1573(79)90060-7},
	abstract = {For beginners: This review tries to explain percolation through the cluster properties; it can also be used as an introduction to critical phenomena at other phase transitions for readers not familiar with scaling theory. In percolation each site of a periodic lattice is randomly occupied with probability p or empty with probability 1−p. An s-cluster is a group of s occupied sites connected by nearest-neighbor distances; the number of empty nearest neighbors of cluster sites is the perimeter t. For p above pc also one infinite cluster percolates through the lattice. How do the properties of s-clusters depend on s, and how do they feel the influence of the phase transition at p = pc? The answers to these questions are given by various methods (in particular computer simulations) and are interpreted by the so-called scaling theory of phase transitions. The results presented here suggest a qualitative difference of cluster structures above and below pc: Above p c some cluster properties suggest the existence of a cluster surface varying as s23 in three dimensions, but below pc these “surface” contributions are proportional to s. We suggest therefore that very large clusters above pc (but not at and below pc) behave like large clusters of Swiss cheese: Inspite of many internal holes the overall cluster shape is roughly spherical, similar to raindrops. For experts: Scaling theory suggests for large clusters near the percolation threshold pc that the average cluster numbers n s vary as s−τƒ(z), with z ≡ (p − pc)sσ. Analogously the average cluster perimeter is ts = s · (1 − p)/p + sσ · ψ1(z), the average cluster radius Rs varies as sσv · R1(z), and the density profile Ds(r), which depends also on the distance r from the cluster center, varies as s−1δ· D̃1(rs−σv, z). These assumptions relate the seven critical exponents α,β,γ,δ,v,σ,τ in d dimensions through the well-known five scaling laws 2 − α = γ + 2β = βδ + β = dv = β + 1σ = (τ − 1)/σ, leaving only two exponents as independent variables to be fitted by “experiment” and not predicted by scaling theory. For the lattice “animals”, i.e. the number gst of geometrically different cluster configurations, a modified scaling assumption is derived: gstsst1/(s + t)s + 1 ∝ s−τ−12 · ƒ(z), with z ∝ (ac − t/s)sσ and ac = (1 − pc)/pc. All these expressions are variants of the general scaling idea for second-order phase transitions that a function g(x,y) of two critical variables takes the homogeneous form xcG(x/yb) near the critical point, with two free exponents b and c and a scaling function G of a single variable. These assumptions, which may be regarded as generalizations of the Fisher droplet model, are tested “experimentally” by Monte Carlo simulation, series expansion, renormalization group technique, and exact inequalities. In particular, detailed Monte Carlo evidence of Hoshen et al. and Leath and Reich is presented for the scaling of cluster numbers in two and three dimensions. If the cluster size s goes to infinity at fixed concentration p, not necessarily close to pc, three additional exponents ξ, θ, ϱ are defined by: cluster numbers ∝ s−θ exp(−const · sξ) and cluster radii ∝ sϱ. These exponents are different on both sides of the phase transition; for example ξ(p {\textless} pc) = 1 and ξ(p {\textgreater} pc) = 1 − 1/d was found from inequalities, series and Monte Carlo data. The behavior of θ and of ϱ(p {\textless} pc) remains to be explained by scaling theory. This article does not cover experimental applications, correlation functions and “classical” (mean field, Bethe lattice, effective medium) theories. For the reader to whom this abstract is too short and the whole article is too long we recommend sections 1 and 3.},
	number = {1},
	urldate = {2018-04-20},
	journal = {Physics Reports},
	author = {Stauffer, D.},
	month = jul,
	year = {1979},
	pages = {1--74},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/KTNA6MWQ/Stauffer - 1979 - Scaling theory of percolation clusters.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/FYC4TRJZ/0370157379900607.html:text/html}
}

@article{bruce_coupled_1975,
	title = {Coupled order parameters, symmetry-breaking irrelevant scaling fields, and tetracritical points},
	volume = {11},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.11.478},
	doi = {10.1103/PhysRevB.11.478},
	abstract = {The phase diagrams of systems described by a Hamiltonian containing an anisotropic quadratic term of the form 12gΣα=1ncα∫→xS2α(→x), and a cubic anisotropic term νΣα=1n∫→xS4α(→x), are studied using mean-field theory, scaling theory, and expansions in ε(=4−d) and 1n. Here, Sα(→x) (a=1, …, n) is a local n-component ordering variable. Systems to which the analysis is applicable include perovskite crystals, stressed along the [100] direction (n=3), anisotropic antiferromagnets in a uniform field, uniaxially anisotropic ferromagnets, ferroelectric ferromagnets and crystalline 4He(n=2). When g=0 and T=Tc these systems undergo a phase transition that may be associated (for small n) with the Heisenberg fixed point (ν∗=0) or (otherwise) with the cubic fixed point (ν∗{\textgreater}0) of the renormalization group. Although ν is an "irrelevant variable" in the former case, it is found to have important effects. For ν{\textless}0, the point g=0, T=Tc represents a bicritical point in the g−T plane, at which a first-order "spin-flop" line (separating two distinct ordered phases) meets two critical lines. For ν{\textgreater}0, the "flop" line splits into two critical lines, associated with transitions between each of the ordered phases and a new intermediate phase; the point T=Tc, g=0 is then tetracritical. The shape of the boundary of the intermediate phase is given by T=T2(g, ν) with [Tc−T2(g, ν)]∼(gν)1ψ2, where ψ2=φg−φν (if the tetracritical point is Heisenberg-like) or ψ2=φCg (if it is cubic). Here, φg, φν, and φCg are appropriate crossover exponents associated with the two symmetry-breaking perturbations. The phase diagram of [111] -stressed perovskites is also discussed and the experimental situation briefly reviewed.},
	number = {1},
	urldate = {2018-04-24},
	journal = {Physical Review B},
	author = {Bruce, Alastair D. and Aharony, Amnon},
	month = jan,
	year = {1975},
	pages = {478--499},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/9MKKQASE/PhysRevB.11.html:text/html;Bruce and Aharony - 1975 - Coupled order parameters, symmetry-breaking irrele.pdf:/home/pants/.zotero/data/storage/IMSQ5NFW/Bruce and Aharony - 1975 - Coupled order parameters, symmetry-breaking irrele.pdf:application/pdf}
}

@article{manuel_carmona_$n$-component_2000,
	title = {\${N}\$-component {Ginzburg}-{Landau} {Hamiltonian} with cubic anisotropy: {A} six-loop study},
	volume = {61},
	shorttitle = {\${N}\$-component {Ginzburg}-{Landau} {Hamiltonian} with cubic anisotropy},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.61.15136},
	doi = {10.1103/PhysRevB.61.15136},
	abstract = {We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N{\textgreater}Nc, Nc=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is ≲1\% in the case of γ and ν). Moreover, the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly decaying scaling corrections with exponent ω2=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent ω2=0.103(8). These conclusions are confirmed by a similar analysis of the five-loop ε expansion. A constrained analysis, which takes into account that Nc=2 in two dimensions, gives Nc=2.87(5).},
	number = {22},
	urldate = {2018-04-24},
	journal = {Physical Review B},
	author = {Manuel Carmona, José and Pelissetto, Andrea and Vicari, Ettore},
	month = jun,
	year = {2000},
	pages = {15136--15151},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/FMBHR6TG/PhysRevB.61.html:text/html;Full Text PDF:/home/pants/.zotero/data/storage/EZGKPAUL/Manuel Carmona et al. - 2000 - \$N\$-component Ginzburg-Landau Hamiltonian with cub.pdf:application/pdf}
}

@article{evertz_stochastic_1991,
	title = {Stochastic cluster algorithms for discrete gaussian ({SOS}) models},
	volume = {254},
	issn = {0370-2693},
	url = {http://www.sciencedirect.com/science/article/pii/037026939190418P},
	doi = {10.1016/0370-2693(91)90418-P},
	abstract = {We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm.},
	number = {1},
	urldate = {2018-04-25},
	journal = {Physics Letters B},
	author = {Evertz, Hans Gerd and Hasenbusch, Martin and Marcu, Mihail and Pinn, Klaus and Solomon, Sorin},
	month = jan,
	year = {1991},
	pages = {185--191},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/I8XRWWAF/Evertz et al. - 1991 - Stochastic cluster algorithms for discrete gaussia.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/2HIT7KGW/037026939190418P.html:text/html}
}

@article{blankschtein_fluctuation-induced_1982,
	title = {Fluctuation-induced first-order transitions and symmetry-breaking fields: {The} \$n=3\$-component cubic model},
	volume = {25},
	shorttitle = {Fluctuation-induced first-order transitions and symmetry-breaking fields},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.25.6939},
	doi = {10.1103/PhysRevB.25.6939},
	abstract = {The effects of an off-diagonal quadratic symmetry-breaking field, g, on a three-component (n=3) cubic model with no accessible fixed points are studied. It is shown that this perturbation induces a crossover from first-order to continuous transition. Depending upon the initial values of the parameters characterizing the model, two types of (g,T) phase diagrams are possible, both of which are rather complex, exhibiting tricritical, critical, and critical end points. The (g,T) phase diagrams are studied using large-g expansion, mean-field theory, and renormalization-group analysis. A universal amplitude ratio associated with the critical end points is calculated to leading (zeroth) order in ε=4−d. The phase diagrams are predicted to be realizable in certain n=3 cubic crystals undergoing structural phase transitions, such as BaTiO3, RbCaF3, and KMnF3.},
	number = {11},
	urldate = {2018-04-25},
	journal = {Physical Review B},
	author = {Blankschtein, Daniel and Mukamel, David},
	month = jun,
	year = {1982},
	pages = {6939--6951},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/KE9V2NH2/PhysRevB.25.html:text/html;Blankschtein and Mukamel - 1982 - Fluctuation-induced first-order transitions and sy.pdf:/home/pants/.zotero/data/storage/UXSNRJXE/Blankschtein and Mukamel - 1982 - Fluctuation-induced first-order transitions and sy.pdf:application/pdf}
}

@article{caracciolo_wolff-type_1993,
	title = {Wolff-type embedding algorithms for general nonlinear σ-models},
	volume = {403},
	issn = {0550-3213},
	url = {http://www.sciencedirect.com/science/article/pii/055032139390044P},
	doi = {10.1016/0550-3213(93)90044-P},
	abstract = {We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on A Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that, at least for an asymptotically free model, such an algorithm can have a dynamic critical exponent z « 2 only if the embedding is based on an (involutive) isometry of M whose fixed-point manifold has codimension 1. Such an isometry exist only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield zint,M2 = 1.5±0.5 (sujective 68\% confidence interval), in agreement with our heuristic argument.},
	number = {1},
	urldate = {2018-04-25},
	journal = {Nuclear Physics B},
	author = {Caracciolo, Sergio and Edwards, Robert G. and Pelissetto, Andrea and Sokal, Alan D.},
	month = aug,
	year = {1993},
	pages = {475--541},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/WSZ7RUI5/Caracciolo et al. - 1993 - Wolff-type embedding algorithms for general nonlin.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/MEJNDW2B/055032139390044P.html:text/html}
}

@article{caracciolo_generalized_1991,
	title = {Generalized {Wolff}-type embedding algorithms for nonlinear σ-models},
	volume = {20},
	issn = {0920-5632},
	url = {http://www.sciencedirect.com/science/article/pii/092056329190883G},
	doi = {10.1016/0920-5632(91)90883-G},
	abstract = {We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that such an algorithm can have dynamic critical exponent z ⪡ 2 only if the embedding is based on an involutive isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.},
	urldate = {2018-04-25},
	journal = {Nuclear Physics B - Proceedings Supplements},
	author = {Caracciolo, Sergio and Edwards, Robert G. and Pelissetto, Andrea and Sokal, Alan D.},
	month = may,
	year = {1991},
	pages = {72--75},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/CADBLAPP/Caracciolo et al. - 1991 - Generalized Wolff-type embedding algorithms for no.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/XW9KUK53/092056329190883G.html:text/html}
}

@article{dotsenko_cluster_1991,
	title = {Cluster {Monte} {Carlo} algorithms for random {Ising} models},
	volume = {170},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/037843719190045E},
	doi = {10.1016/0378-4371(91)90045-E},
	abstract = {Variations of the Swendsen-Wang and Wolff cluster flip algorithms are proposed to perform Monte Carlo simulations of Ising models with random bonds and random fields, including systems with frustration. The new methods are tested by applying them to small lattices and comparing the results with exact data.},
	number = {2},
	urldate = {2018-05-09},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Dotsenko, Vl. S. and Selke, W. and Talapov, A. L.},
	month = jan,
	year = {1991},
	keywords = {monte-carlo, rfim, cluster-algorithm},
	pages = {278--281},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/ZULKCCN9/Dotsenko et al. - 1991 - Cluster Monte Carlo algorithms for random Ising mo.pdf:application/pdf;ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/39ZPGDAE/Dotsenko et al. - 1991 - Cluster Monte Carlo algorithms for random Ising mo.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/7Z9PAX48/037843719190045E.html:text/html;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/8YGYCZZ8/037843719190045E.html:text/html}
}

@incollection{rieger_monte_1995,
	title = {Monte {Carlo} {Studies} of {Ising} {Spin} {Glasses} and {Random} {Field} {Systems}},
	url = {http://adsabs.harvard.edu/abs/1995arc2.book..295R},
	abstract = {We review recent numerical progress in the study of finite dimensional 
strongly disordered magnetic systems like spin glasses and random field
systems. In particular we report in some detail results for the critical
properties and the non-equilibrium dynamics of Ising spin glasses.
Furthermore we present an overview of recent investigations on the
random field Ising model and finally of quantum spin glasses.},
	urldate = {2018-05-09},
	booktitle = {Annual {Reviews} of {Computational} {Physics} {II}. {Edited} by {STAUFFER} {DIETRICH}. {Published} by {World} {Scientific} {Publishing} {Co}. {Pte}. {Ltd}., 1995. {ISBN} \#9789812831149, pp. 295-341},
	author = {Rieger, Heiko},
	year = {1995},
	doi = {10.1142/9789812831149_0007},
	pages = {295--341},
	file = {arXiv\:cond-mat/9411017 PDF:/home/pants/.zotero/data/storage/NTUDS8GH/Rieger - 1995 - Monte Carlo Studies of Ising Spin Glasses and Rand.pdf:application/pdf}
}

@article{mermin_topological_1979,
	title = {The topological theory of defects in ordered media},
	volume = {51},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.51.591},
	doi = {10.1103/RevModPhys.51.591},
	abstract = {Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology. The aim is to make more readily accessible to physicists the recent applications of homotopy theory to the study of defects in ordered media. Although many physical examples are woven into the development of the subject, the focus is on mathematical pedagogy rather than on a systematic review of applications.},
	number = {3},
	urldate = {2018-05-09},
	journal = {Reviews of Modern Physics},
	author = {Mermin, N. D.},
	month = jul,
	year = {1979},
	pages = {591--648},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/GD9PHBAV/RevModPhys.51.html:text/html;Mermin - 1979 - The topological theory of defects in ordered media.pdf:/home/pants/.zotero/data/storage/ZJE9JPN6/Mermin - 1979 - The topological theory of defects in ordered media.pdf:application/pdf}
}

@article{martin-mayor_tethered_2011,
	title = {Tethered {Monte} {Carlo}: {Managing} {Rugged} {Free}-{Energy} {Landscapes} with a {Helmholtz}-{Potential} {Formalism}},
	volume = {144},
	issn = {1572-9613},
	shorttitle = {Tethered {Monte} {Carlo}},
	url = {https://doi.org/10.1007/s10955-011-0261-4},
	doi = {10.1007/s10955-011-0261-4},
	abstract = {Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total magnitude (system+reservoir) is conserved. The reservoir is actually integrated out, which leaves us with a fluctuation-dissipation formalism that allows us to recover the appropriate Helmholtz effective potential with great accuracy. These methods are demonstrating a remarkable flexibility. In fact, we illustrate two very different applications: hard spheres crystallization and the phase transition of the diluted antiferromagnet in a field (the physical realization of the random field Ising model). The tethered approach holds the promise to transform cartoon drawings of corrugated free-energy landscapes into real computations. Besides, it reduces the algorithmic dynamic slowing-down, probably because the conservation law holds non-locally.},
	language = {en},
	number = {3},
	urldate = {2018-09-19},
	journal = {Journal of Statistical Physics},
	author = {Martin-Mayor, V. and Seoane, B. and Yllanes, D.},
	month = aug,
	year = {2011},
	keywords = {Effective potential, Monte Carlo methods, Barriers},
	pages = {554--596},
	file = {Martin-Mayor et al. - 2011 - Tethered Monte Carlo Managing Rugged Free-Energy .pdf:/home/pants/.zotero/data/storage/HEICZ4EE/Martin-Mayor et al. - 2011 - Tethered Monte Carlo Managing Rugged Free-Energy .pdf:application/pdf}
}

@article{martin-mayor_cluster_2009,
	title = {Cluster {Monte} {Carlo} algorithm with a conserved order parameter},
	volume = {80},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.80.015701},
	doi = {10.1103/PhysRevE.80.015701},
	abstract = {We propose a cluster simulation algorithm for statistical ensembles with fixed order parameter. We use the tethered ensemble, which features Helmholtz’s effective potential rather than Gibbs’s free energy and in which canonical averages are recovered with arbitrary accuracy. For the D=2,3 Ising model our method’s critical slowing down is comparable to that of canonical cluster algorithms. Yet, we can do more than merely reproduce canonical values. As an example, we obtain a competitive value for the 3D Ising anomalous dimension from the maxima of the effective potential.},
	number = {1},
	urldate = {2018-09-19},
	journal = {Physical Review E},
	author = {Martin-Mayor, V. and Yllanes, D.},
	month = jul,
	year = {2009},
	pages = {015701},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/2USVICMH/PhysRevE.80.html:text/html;Martin-Mayor and Yllanes - 2009 - Cluster Monte Carlo algorithm with a conserved ord.pdf:/home/pants/.zotero/data/storage/7G4SJC85/Martin-Mayor and Yllanes - 2009 - Cluster Monte Carlo algorithm with a conserved ord.pdf:application/pdf}
}

@article{ossola_dynamic_2004,
	title = {Dynamic critical behavior of the {Swendsen}–{Wang} algorithm for the three-dimensional {Ising} model},
	volume = {691},
	issn = {0550-3213},
	url = {http://www.sciencedirect.com/science/article/pii/S0550321304003098},
	doi = {10.1016/j.nuclphysb.2004.04.026},
	abstract = {We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen–Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the “energy-like” observables, we find zint,N=zint,E=zint,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68\% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68\% subjective confidence interval). For the “susceptibility-like” observables, we find zint,M2=zint,S2=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find zexp≈0.481. Our data are consistent with the Coddington–Baillie conjecture zSW=β/ν≈0.5183, especially if it is interpreted as referring to zexp.},
	number = {3},
	urldate = {2018-09-19},
	journal = {Nuclear Physics B},
	author = {Ossola, Giovanni and Sokal, Alan D.},
	month = jul,
	year = {2004},
	keywords = {Ising model, Cluster algorithm, Autocorrelation time, Dynamic critical exponent, Monte Carlo, Potts model, Swendsen–Wang algorithm},
	pages = {259--291},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/MKA8WYZZ/Ossola and Sokal - 2004 - Dynamic critical behavior of the Swendsen–Wang alg.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/YHGX7CDT/S0550321304003098.html:text/html}
}

@article{ala-nissila_numerical_1994,
	title = {Numerical studies of the two-dimensional {XY} model with symmetry-breaking fields},
	volume = {50},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.50.12692},
	doi = {10.1103/PhysRevB.50.12692},
	abstract = {We present results of numerical studies of the two-dimensional XY model with four- and eightfold symmetry-breaking fields. This model has recently been shown to describe hydrogen-induced reconstruction on the W(100) surface. Based on mean-field and renormalization-group arguments, we first show how the interplay between the anisotropy fields can give rise to different phase transitions in the model. When the fields are compatible with each other there is a continuous phase transition when the fourth-order field is varied from negative to positive values. This transition becomes discontinuous at low temperatures. These two regimes are separated by a multicritical point. In the case of competing four- and eightfold fields, the first-order transition at low temperatures opens up into two Ising transitions. We then use numerical methods to accurately locate the position of the multicritical point, and to verify the nature of the transitions. The different techniques used include Monte Carlo histogram methods combined with finite-size scaling analysis, the real-space Monte Carlo renormalization-group method, and the Monte Carlo transfer-matrix method. Our numerical results are in good agreement with the theoretical arguments.},
	number = {17},
	urldate = {2018-09-25},
	journal = {Physical Review B},
	author = {Ala-Nissila, T. and Granato, E. and Kankaala, K. and Kosterlitz, J. M. and Ying, S.-C.},
	month = nov,
	year = {1994},
	pages = {12692--12701},
	file = {Ala-Nissila et al. - 1994 - Numerical studies of the two-dimensional XY model .pdf:/home/pants/.zotero/data/storage/2C3RYCHG/Ala-Nissila et al. - 1994 - Numerical studies of the two-dimensional XY model .pdf:application/pdf;APS Snapshot:/home/pants/.zotero/data/storage/YU2G86C5/PhysRevB.50.html:text/html}
}

@article{kankaala_theory_1993,
	title = {Theory of adsorbate-induced surface reconstruction on {W}(100)},
	volume = {47},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.47.2333},
	doi = {10.1103/PhysRevB.47.2333},
	abstract = {We report results of a theoretical study on an adsorbate-induced surface reconstruction. Hydrogen adsorption on a W(100) surface causes a switching transition in the symmetry of the displacements of the W atoms within the ordered c(2×2) phase. This transition is modeled by an effective Hamiltonian, where the hydrogen degrees of freedom are integrated out. Based on extensive Monte Carlo renormalization-group calculations we show that the switching transition is of second order at high temperatures and of first order at low temperatures. This behavior is qualitatively explained in terms of an XY model where there is an interplay between fourfold and eightfold anisotropy fields. We also compare the calculated phase diagrams with a simple mean-field theory.},
	number = {4},
	urldate = {2018-09-25},
	journal = {Physical Review B},
	author = {Kankaala, Kari and Ala-Nissila, Tapio and Ying, See-Chen},
	month = jan,
	year = {1993},
	pages = {2333--2343},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/EQCT6K8H/PhysRevB.47.html:text/html;Kankaala et al. - 1993 - Theory of adsorbate-induced surface reconstruction.pdf:/home/pants/.zotero/data/storage/8DGX9H9Y/Kankaala et al. - 1993 - Theory of adsorbate-induced surface reconstruction.pdf:application/pdf}
}

@article{selinger_theory_1988,
	title = {Theory of {Hexatic}-to-{Hexatic} {Transitions}},
	volume = {61},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.416},
	doi = {10.1103/PhysRevLett.61.416},
	abstract = {A theory of transitions between tilted hexatic-I and -F phases in liquid-crystal films is developed. A renormalization-group analysis leads to four tilted hexatic phases: the hexatic-I and -F phases, an intermediate hexatic-L phase, and an unlocked phase. All these phases except the unlocked phase also exist if the films are crystalline rather than hexatic. These results are consistent with recent experiments on thermotropic and lyotropic liquid crystals.},
	number = {4},
	urldate = {2018-09-25},
	journal = {Physical Review Letters},
	author = {Selinger, Jonathan V. and Nelson, David R.},
	month = jul,
	year = {1988},
	pages = {416--419},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/59CAGAAM/PhysRevLett.61.html:text/html;Selinger and Nelson - 1988 - Theory of Hexatic-to-Hexatic Transitions.pdf:/home/pants/.zotero/data/storage/EHI5X23X/Selinger and Nelson - 1988 - Theory of Hexatic-to-Hexatic Transitions.pdf:application/pdf}
}

@article{dierker_consequences_1986,
	title = {Consequences of {Bond}-{Orientational} {Order} on the {Macroscopic} {Orientation} {Patterns} of {Thin} {Tilted} {Hexatic} {Liquid}-{Crystal} {Films}},
	volume = {56},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.56.1819},
	doi = {10.1103/PhysRevLett.56.1819},
	abstract = {By use of depolarized laser relection microscopy, unique textural defects have been observed in thin tilted hexatic liquid-crystal films which result from their bond-orientational order. The temperature dependence of the bond-orientational elasticity can be deduced from these textural patterns and is in qualitative agreement with the theory of two-dimensional melting. The effects of molecular chirality and film thickness on the defect textures is also reported along with observations on the polygonization of the two-dimensional crystalline phase.},
	number = {17},
	urldate = {2018-09-25},
	journal = {Physical Review Letters},
	author = {Dierker, S. B. and Pindak, R. and Meyer, R. B.},
	month = apr,
	year = {1986},
	pages = {1819--1822},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/A8T7IR63/PhysRevLett.56.html:text/html;Dierker et al. - 1986 - Consequences of Bond-Orientational Order on the Ma.pdf:/home/pants/.zotero/data/storage/9XEH86XP/Dierker et al. - 1986 - Consequences of Bond-Orientational Order on the Ma.pdf:application/pdf}
}

@misc{bierbaum_ising.js_2016,
	title = {Ising.js},
	url = {https://mattbierbaum.github.io/ising.js/},
	urldate = {2018-09-25},
	author = {Bierbaum, Matthew K.},
	year = {2016},
	note = {https://github.com/mattbierbaum/ising.js/}
}

@article{bortz_new_1975,
	title = {A new algorithm for {Monte} {Carlo} simulation of {Ising} spin systems},
	volume = {17},
	issn = {0021-9991},
	url = {http://www.sciencedirect.com/science/article/pii/0021999175900601},
	doi = {10.1016/0021-9991(75)90060-1},
	abstract = {We describe a new algorithm for Monte Carlo simulation of Ising spin systems and present results of a study comparing the speed of the new technique to that of a standard technique applied to a square lattice of 6400 spins evolving via single spin flips. We find that at temperatures T {\textless} Tc, the critical temperature, the new technique is faster than the standard technique, being ten times faster at T = 0.588 Tc. We expect that the new technique will be especially valuable in Monte Carlo simulation of the time evolution of binary alloy systems. The new algorithm is essentially a reorganization of the standard algorithm. It accounts for the a priori probability of changing spins before, rather than after, choosing the spin or spins to change.},
	number = {1},
	urldate = {2018-10-04},
	journal = {Journal of Computational Physics},
	author = {Bortz, A. B. and Kalos, M. H. and Lebowitz, J. L.},
	month = jan,
	year = {1975},
	pages = {10--18},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/MZB8RWET/Bortz et al. - 1975 - A new algorithm for Monte Carlo simulation of Isin.pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/5LZNTCRU/0021999175900601.html:text/html}
}

@article{zhang_melting_1991,
	title = {Melting of monolayer argon adsorbed on a graphite substrate},
	volume = {43},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.43.938},
	doi = {10.1103/PhysRevB.43.938},
	abstract = {Argon films physisorbed on a graphite substrate were studied at coverages near monolayer completion using high-resolution vapor-pressure isotherms. New experimental evidence is presented that is consistent with a picture of monolayer argon melting via a two-stage process involving the existence of an intermediate phase with short-range spatial order and solidlike properties. These findings resolve the interpretational inconsistensies concerning the melting of argon films which presently exist between the earlier thermodynamic studies and various microscopic scattering measurements.},
	number = {1},
	urldate = {2018-10-12},
	journal = {Physical Review B},
	author = {Zhang, Q. M. and Larese, J. Z.},
	month = jan,
	year = {1991},
	pages = {938--946},
	file = {APS Snapshot:/home/pants/.zotero/data/storage/NCJ8EBM9/PhysRevB.43.html:text/html;Zhang and Larese - 1991 - Melting of monolayer argon adsorbed on a graphite .pdf:/home/pants/.zotero/data/storage/MZTKK99U/Zhang and Larese - 1991 - Melting of monolayer argon adsorbed on a graphite .pdf:application/pdf}
}

@misc{kent-dobias_wolff_2018,
	title = {Wolff},
	url = {https://git.kent-dobias.com/wolff/},
	abstract = {Efficiently simulate spin models using a generalized Wolff algorithm.},
	author = {Kent-Dobias, Jaron},
	year = {2018},
	note = {https://git.kent-dobias.com/wolff/}
}

@article{hasenbusch_improved_1990,
	title = {Improved estimators for a cluster updating of {O}(n) spin models},
	volume = {333},
	issn = {0550-3213},
	url = {http://www.sciencedirect.com/science/article/pii/055032139090052F},
	doi = {10.1016/0550-3213(90)90052-F},
	abstract = {We present a generalisation of the cluster algorithm introduced by Swendsen and Wang to O(n) spin models. We have found an improved estimator of the susceptibility and the two-point function for this algorithm. Numerical simulations were performed for the XY model and the O(4) model on lattices up to 2562 to check the efficiency of the algorithm and the estimators. We found no indication for critical slowing down.},
	number = {2},
	urldate = {2018-10-20},
	journal = {Nuclear Physics B},
	author = {Hasenbusch, Martin},
	month = mar,
	year = {1990},
	pages = {581--592},
	file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/HMXWXQKA/Hasenbusch - 1990 - Improved estimators for a cluster updating of O(n).pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/FR2HQ3GJ/055032139090052F.html:text/html}
}