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diff --git a/hidden_order.bib b/hidden_order.bib index 3b779ed..2194a59 100644 --- a/hidden_order.bib +++ b/hidden_order.bib @@ -92,6 +92,22 @@ file = {/home/pants/Zotero/storage/FQWHY9TF/Hornreich - 1980 - The Lifshitz point Phase diagrams and critical be.pdf} } +@article{guida_critical_1998, + title = {Critical Exponents of the {{N}}-Vector Model}, + volume = {31}, + issn = {0305-4470}, + 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}, + journal = {Journal of Physics A: Mathematical and General}, + doi = {10.1088/0305-4470/31/40/006}, + author = {Guida, R. and {Zinn-Justin}, J.}, + year = {1998}, + keywords = {_tablet}, + pages = {8103}, + file = {/home/pants/Zotero/storage/K468APXL/Guida and Zinn-Justin - 1998 - Critical exponents of the N-vector model.pdf} +} + @article{varshni_temperature_1970, title = {Temperature {{Dependence}} of the {{Elastic Constants}}}, volume = {2}, @@ -514,4 +530,96 @@ thermodynamics from a hidden order parameter.}, file = {/home/pants/Zotero/storage/GBYIESIW/Hornreich et al_1975_Critical Behavior at the Onset of.pdf;/home/pants/Zotero/storage/KBYQHWSH/PhysRevLett.35.html} } +@article{selke_monte_1978, + title = {Monte Carlo Calculations near a Uniaxial {{Lifshitz}} Point}, + volume = {29}, + issn = {1431-584X}, + abstract = {The Monte Carlo method is applied to a threedimensional Ising model with nearest neighbour ferromagnetic interactions and next nearest neighbour antiferromagnetic interactions along one axis only. Special emphasis is given to the critical behaviour near the Lifshitz point.}, + language = {en}, + number = {2}, + journal = {Zeitschrift f{\"u}r Physik B Condensed Matter}, + doi = {10.1007/BF01313198}, + author = {Selke, Walter}, + month = jun, + year = {1978}, + keywords = {Complex System,Neural Network,Spectroscopy,State Physics,Monte Carlo Method}, + pages = {133-137}, + file = {/home/pants/Zotero/storage/5NRZEWP8/Selke_1978_Monte carlo calculations near a uniaxial Lifshitz point.pdf} +} + +@article{hornreich_critical_1975-1, + title = {Critical Exponents at a {{Lifshitz}} Point to {{O}}(1/n)}, + volume = {55}, + issn = {0375-9601}, + abstract = {The critical exponents at a general Lifshitz point are calculated in the spherical model limit, as are those of an isotropic Lifshitz point to O(1/n). These results are in exact agreement in the overlap region with those obtained using an {$\epsilon$}-expansion.}, + number = {5}, + journal = {Physics Letters A}, + doi = {10.1016/0375-9601(75)90465-X}, + author = {Hornreich, R. M. and Luban, M. and Shtrikman, S.}, + month = dec, + year = {1975}, + pages = {269-270}, + file = {/home/pants/Zotero/storage/RED39SK4/Hornreich et al_1975_Critical exponents at a Lifshitz point to O(1-n).pdf;/home/pants/Zotero/storage/X8UJ5CHZ/037596017590465X.html} +} + +@article{hornreich_exactly_1977, + title = {Exactly Solvable Model Exhibiting a Multicritical Point}, + volume = {86}, + issn = {0378-4371}, + abstract = {A hypercubic d-dimensional lattice of spins with nearest neighbor ferromagnetic coupling and next nearest neighbor antiferromagnetic coupling along a single axis is studied in the spherical model limit (n\textrightarrow{$\infty$}) and is found to exhibit a multicritical point of the uniaxial Lifshitz type. The shape of the {$\lambda$} line is calculated explicitly in the vicinity of the multicritical point, and analytic expressions are given for the shift exponent {$\psi$}(d) and its amplitudes A{$\pm$}(d). The amplitude A\_(d) changes sign for d = 3.}, + number = {2}, + journal = {Physica A: Statistical Mechanics and its Applications}, + doi = {10.1016/0378-4371(77)90042-5}, + author = {Hornreich, R. M. and Luban, Marshall and Shtrikman, S.}, + month = feb, + year = {1977}, + pages = {465-470}, + file = {/home/pants/Zotero/storage/5MFN7M9Z/Hornreich et al_1977_Exactly solvable model exhibiting a multicritical point.pdf;/home/pants/Zotero/storage/CZNV72TI/0378437177900425.html} +} + +@article{nicoll_renormalization_1976, + title = {Renormalization Group Calculation for Critical Points of Higher Order with General Propagator}, + volume = {58}, + issn = {0375-9601}, + abstract = {We give first order perturbation results for the critical point exponents at order O critical points with anisotropic propagators. The exponent {$\eta$} is calculated to second order for isotropic propagators, and all O; 1/n expansion results are given for O = 2.}, + number = {1}, + journal = {Physics Letters A}, + doi = {10.1016/0375-9601(76)90527-2}, + author = {Nicoll, J. F. and Tuthill, G. F. and Chang, T. S. and Stanley, H. E.}, + month = jul, + year = {1976}, + pages = {1-2}, + file = {/home/pants/Zotero/storage/55AS69UD/Nicoll et al_1976_Renormalization group calculation for critical points of higher order with.pdf;/home/pants/Zotero/storage/L6WH4D36/0375960176905272.html} +} + +@article{nicoll_onset_1977, + title = {Onset of Helical Order}, + volume = {86-88}, + issn = {0378-4363}, + abstract = {Renormalization group methods are used to describe systems which model critical phenomena at the onset of helical order. This onset is marked by a change in the ``bare propagator'' used in perturbation theory from a k2-dependence to a more general form. We consider systems which in the non-helical region exhibit O simultaneously critical phases. Results are given to first order in an {$\epsilon$}-expansion. For the isotropic case of k2L dependence and O = 2, we give {$\eta$} to first order in 1/n for d- {$\leqslant$} d {$\leqslant$} d+ where d+- are upper and lower borderline dimensions.}, + journal = {Physica B+C}, + doi = {10.1016/0378-4363(77)90620-9}, + author = {Nicoll, J. F. and Tuthill, G. F. and Chang, T. S. and Stanley, H. E.}, + month = jan, + year = {1977}, + pages = {618-620}, + file = {/home/pants/Zotero/storage/ZLV5YFH6/Nicoll et al_1977_Onset of helical order.pdf;/home/pants/Zotero/storage/84ZZT6CN/0378436377906209.html} +} + +@article{garel_commensurability_1976, + title = {Commensurability Effects on the Critical Behaviour of Systems with Helical Ordering}, + volume = {9}, + issn = {0022-3719}, + abstract = {The critical behaviour of an m-component spin system with helical ordering is studied using the renormalization group method to order epsilon 2 (where epsilon =4-d). For m=1 and 2 the system is equivalent to a 2m-vector model. For m=3 a first-order transition is expected. The effect of the commensurability of the helical structure with the lattice has been considered and is shown in certain situations to change the order of the transition.}, + language = {en}, + number = {10}, + journal = {Journal of Physics C: Solid State Physics}, + doi = {10.1088/0022-3719/9/10/001}, + author = {Garel, T. and Pfeuty, P.}, + month = may, + year = {1976}, + pages = {L245--L249}, + file = {/home/pants/Zotero/storage/34KTXA6I/Garel_Pfeuty_1976_Commensurability effects on the critical behaviour of systems with helical.pdf} +} + |