From a8f8a3fad2d07780c48db7e15036dec5ea8ab90d Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 15 May 2018 10:58:29 -0400 Subject: new paragraph --- data/autocorrelation.dat | 44 +++--- fig_clusters_ising2d.eps | 4 +- fig_correlation-temp.tex | 4 +- fig_correlation.tex | 4 +- fig_correlation_collapse-hL.tex | 309 ++++++++++++++++++++-------------------- fig_metastable.tex | 4 +- monte-carlo.bib | 6 +- monte-carlo.pdf | Bin 191228 -> 192821 bytes monte-carlo.tex | 15 +- prl-paragraph.txt | 1 + 10 files changed, 199 insertions(+), 192 deletions(-) create mode 100644 prl-paragraph.txt diff --git a/data/autocorrelation.dat b/data/autocorrelation.dat index 2d4fcb2..173b648 100644 --- a/data/autocorrelation.dat +++ b/data/autocorrelation.dat @@ -79,16 +79,16 @@ 64 2.26918531421 1.25893 0.5478998413201179 0.0003065498105019881 64 2.26918531421 5.01187 0.501515121086641 0 -128 2.26918531421 0.00001 2.7178897501663415 0.07196068539143026 -128 2.26918531421 0.0000199526 2.695587356709051 0.07951391257640775 -128 2.26918531421 0.0000398107 2.6764940796506007 0.05472122690422448 -128 2.26918531421 0.0000794328 2.6421160513407758 0.07209385716975884 -128 2.26918531421 0.000158489 2.5794500241770613 0.05648773213969451 -128 2.26918531421 0.000316228 2.4859007210158097 0.05515668025270037 -128 2.26918531421 0.000630957 2.241640050002785 0.0341814927660582 -128 2.26918531421 0.00125893 1.9947585081079842 0.07967318260134539 -128 2.26918531421 0.00251189 1.7226285000980959 0.015325114441769963 -128 2.26918531421 0.00501187 1.5363538595317479 0.03483822340636096 +128 2.26918531421 0.00001 2.695785688726008 0.041974565130960935 +128 2.26918531421 0.0000199526 2.6693785953694826 0.044332980283103944 +128 2.26918531421 0.0000398107 2.7093423315360625 0.03481903267984265 +128 2.26918531421 0.0000794328 2.668053686652282 0.04116526016506879 +128 2.26918531421 0.000158489 2.642448487552821 0.05450228242647508 +128 2.26918531421 0.000316228 2.489464704102084 0.020670848999044047 +128 2.26918531421 0.000630957 2.253523958724577 0.027374472593511456 +128 2.26918531421 0.00125893 1.9829070316737643 0.0365399462318801 +128 2.26918531421 0.00251189 1.7292013703893456 0.00993970678418459 +128 2.26918531421 0.00501187 1.591537949315759 0.04585204157216723 128 2.26918531421 0.01 1.4264501502084832 0.04722018619065011 128 2.26918531421 0.0199526 1.2112528598082197 0.01374385167550162 128 2.26918531421 0.0398107 1.0605115179682987 0.008591054299916991 @@ -106,16 +106,16 @@ 256 2.26918531421 0.0000794328 3.048790937344986 0.07111471296548877 256 2.26918531421 0.000158489 2.6936331659574626 0.07578811950394938 256 2.26918531421 0.000316228 2.363778914033675 0.06178660367644999 -256 2.26918531421 0.000630957 2.1754451430148865 0.09608622842353752 -256 2.26918531421 0.00125893 1.8641436845768051 0.035031492421004506 -256 2.26918531421 0.00251189 1.923924522183799 0.1775663715437454 -256 2.26918531421 0.00501187 1.4553962657237585 0.007060830110945492 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0.011633658182744238 +256 2.26918531421 0.158489 0.8140323427455325 0.0072566757208961195 +256 2.26918531421 0.316228 0.7801936394930267 0.03408315998924669 +256 2.26918531421 0.630957 0.6297044935263589 0.013064710146296678 +256 2.26918531421 1.25893 0.5614357073329381 0.00393406711122985 256 2.26918531421 2.51189 0.619808411946246 0 diff --git a/fig_clusters_ising2d.eps b/fig_clusters_ising2d.eps index 875e626..cd2d8a3 100644 --- a/fig_clusters_ising2d.eps +++ b/fig_clusters_ising2d.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: fig_clusters_ising2d.tex %%Creator: gnuplot 5.2 patchlevel 2 -%%CreationDate: Wed May 9 17:36:13 2018 +%%CreationDate: Thu May 10 20:47:25 2018 %%DocumentFonts: %%BoundingBox: 50 50 542 252 %%EndComments @@ -441,7 +441,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 2) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed May 9 17:36:13 2018) + /CreationDate (Thu May 10 20:47:25 2018) /DOCINFO pdfmark end } ifelse diff --git a/fig_correlation-temp.tex b/fig_correlation-temp.tex index 5d27d13..db7ab02 100644 --- a/fig_correlation-temp.tex +++ b/fig_correlation-temp.tex @@ -8,7 +8,7 @@ {\GNUPLOTspecial{" %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 5.2 patchlevel 2 -%%CreationDate: Wed May 9 17:24:17 2018 +%%CreationDate: Thu May 10 20:47:25 2018 %%DocumentFonts: %%BoundingBox: 0 0 246 151 %%EndComments @@ -448,7 +448,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 2) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed May 9 17:24:17 2018) + /CreationDate (Thu May 10 20:47:25 2018) /DOCINFO pdfmark end } ifelse diff --git a/fig_correlation.tex b/fig_correlation.tex index a2df150..f5c4d93 100644 --- a/fig_correlation.tex +++ b/fig_correlation.tex @@ -8,7 +8,7 @@ {\GNUPLOTspecial{" %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 5.2 patchlevel 2 -%%CreationDate: Wed May 9 17:24:16 2018 +%%CreationDate: Thu May 10 20:47:25 2018 %%DocumentFonts: %%BoundingBox: 0 0 246 455 %%EndComments @@ -448,7 +448,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 2) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed May 9 17:24:16 2018) + /CreationDate (Thu May 10 20:47:25 2018) /DOCINFO pdfmark end } ifelse diff --git a/fig_correlation_collapse-hL.tex b/fig_correlation_collapse-hL.tex index e42051d..dff56bf 100644 --- a/fig_correlation_collapse-hL.tex +++ b/fig_correlation_collapse-hL.tex @@ -8,7 +8,7 @@ {\GNUPLOTspecial{" %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 5.2 patchlevel 2 -%%CreationDate: Wed May 9 17:24:59 2018 +%%CreationDate: Thu May 10 20:47:25 2018 %%DocumentFonts: %%BoundingBox: 0 0 246 151 %%EndComments @@ -448,7 +448,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 2) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed May 9 17:24:59 2018) + /CreationDate (Thu May 10 20:47:25 2018) /DOCINFO pdfmark end } ifelse @@ -1413,66 +1413,66 @@ stroke 1737 2385 M 62 0 V -62 0 R 62 0 V -.4839 g 1675 2353 M -0 44 V --31 -44 R +.4839 g 1675 2355 M +0 26 V +-31 -26 R 62 0 V --62 44 R +-62 26 R 62 0 V -.4839 g 1804 2343 M -0 50 V --31 -50 R +.4839 g 1804 2346 M +0 28 V +-31 -28 R 62 0 V --62 50 R +-62 28 R 62 0 V -.4839 g 1933 2345 M -0 34 V --31 -34 R +.4839 g 1933 2362 M +0 21 V +-31 -21 R 62 0 V --62 34 R +-62 21 R 62 0 V -.4839 g 2062 2328 M -0 46 V --31 -46 R +.4839 g 2062 2347 M +0 25 V +-31 -25 R 62 0 V --62 46 R +-62 25 R 62 0 V -.4839 g 2191 2313 M -0 36 V --31 -36 R +.4839 g 2191 2334 M +0 35 V +-31 -35 R 62 0 V --62 36 R +-62 35 R 62 0 V -.4839 g 2320 2281 M -0 38 V --31 -38 R +.4839 g 2320 2295 M +0 13 V +-31 -13 R 62 0 V --62 38 R +-62 13 R 62 0 V -.4839 g 2449 2201 M -0 25 V --31 -25 R +.4839 g 2449 2208 M +0 20 V +-31 -20 R 62 0 V --62 25 R +-62 20 R 62 0 V -.4839 g 2578 2082 M -0 67 V --31 -67 R +.4839 g 2578 2095 M +0 31 V +-31 -31 R 62 0 V --62 67 R +-62 31 R 62 0 V -.4839 g 2707 1985 M -0 15 V --31 -15 R +.4839 g 2707 1991 M +0 10 V +-31 -10 R 62 0 V -stroke 2738 1985 M --62 15 R +stroke 2738 1991 M +-62 10 R 62 0 V -.4839 g 2836 1878 M -0 38 V --31 -38 R +.4839 g 2836 1902 M +0 48 V +-31 -48 R 62 0 V --62 38 R +-62 48 R 62 0 V .4839 g 2965 1807 M 0 55 V @@ -1568,74 +1568,77 @@ stroke 2738 1985 M 62 0 V -62 43 R 62 0 V -1 g 2692 1976 M -0 74 V --31 -74 R +1 g 2692 1987 M +0 33 V +-31 -33 R 62 0 V --62 74 R +-62 33 R 62 0 V -1 g 2821 1869 M +1 g 2821 1896 M 0 31 V -31 -31 R 62 0 V -62 31 R 62 0 V -1 g 2950 1830 M -0 155 V --31 -155 R +1 g 2950 1822 M +0 85 V +-31 -85 R 62 0 V --62 155 R +-62 85 R 62 0 V -1 g 3079 1673 M -0 8 V --31 -8 R +1 g 3079 1691 M +0 87 V +-31 -87 R 62 0 V --62 8 R +-62 87 R 62 0 V -1 g 3208 1587 M -0 104 V --31 -104 R +1 g 3208 1631 M +0 55 V +-31 -55 R 62 0 V --62 104 R +-62 55 R 62 0 V -1 g 3337 1496 M -0 57 V --31 -57 R +1 g 3337 1514 M +0 26 V +-31 -26 R 62 0 V --62 57 R +-62 26 R 62 0 V -1 g 3466 1410 M -0 19 V --31 -19 R +1 g 3466 1421 M +0 113 V +-31 -113 R 62 0 V --62 19 R +-62 113 R 62 0 V -1 g 3595 1276 M --31 0 R +1 g 3595 1292 M +0 21 V +-31 -21 R 62 0 V --62 0 R +-62 21 R 62 0 V -1 g 3724 1177 M -0 18 V --31 -18 R +1 g 3724 1183 M +0 15 V +-31 -15 R 62 0 V --62 18 R +-62 15 R 62 0 V -1 g 3853 1066 M -0 149 V --31 -149 R +1 g 3853 1117 M +0 73 V +-31 -73 R 62 0 V --62 149 R +-62 73 R 62 0 V -1 g 3982 948 M --31 0 R +1 g 3982 957 M +0 35 V +-31 -35 R 62 0 V --62 0 R +-62 35 R 62 0 V -1 g 4111 866 M --31 0 R +1 g 4111 873 M +0 12 V +-31 -12 R 62 0 V --62 0 R +-62 12 R 62 0 V 1 g 4240 962 M -31 0 R @@ -1717,16 +1720,16 @@ stroke 2738 1985 M .2258 g 3497 1303 Pnt .2258 g 3626 1207 Pnt .2258 g 3884 1133 Pnt -.4839 g 1675 2375 Pnt -.4839 g 1804 2368 Pnt -.4839 g 1933 2362 Pnt -.4839 g 2062 2351 Pnt -.4839 g 2191 2331 Pnt -.4839 g 2320 2300 Pnt -.4839 g 2449 2214 Pnt -.4839 g 2578 2116 Pnt -.4839 g 2707 1993 Pnt -.4839 g 2836 1897 Pnt +.4839 g 1675 2368 Pnt +.4839 g 1804 2360 Pnt +.4839 g 1933 2372 Pnt +.4839 g 2062 2360 Pnt +.4839 g 2191 2351 Pnt +.4839 g 2320 2302 Pnt +.4839 g 2449 2218 Pnt +.4839 g 2578 2111 Pnt +.4839 g 2707 1996 Pnt +.4839 g 2836 1927 Pnt .4839 g 2965 1835 Pnt .4839 g 3094 1698 Pnt .4839 g 3223 1586 Pnt @@ -1743,18 +1746,18 @@ stroke 2738 1985 M 1 g 2305 2297 Pnt 1 g 2434 2193 Pnt 1 g 2563 2084 Pnt -1 g 2692 2014 Pnt -1 g 2821 1885 Pnt -1 g 2950 1911 Pnt -1 g 3079 1677 Pnt -1 g 3208 1641 Pnt -1 g 3337 1525 Pnt -1 g 3466 1420 Pnt -1 g 3595 1276 Pnt -1 g 3724 1186 Pnt -1 g 3853 1144 Pnt -1 g 3982 948 Pnt -1 g 4111 866 Pnt +1 g 2692 2003 Pnt +1 g 2821 1912 Pnt +1 g 2950 1865 Pnt +1 g 3079 1735 Pnt +1 g 3208 1659 Pnt +1 g 3337 1527 Pnt +1 g 3466 1479 Pnt +1 g 3595 1303 Pnt +1 g 3724 1190 Pnt +1 g 3853 1155 Pnt +1 g 3982 975 Pnt +1 g 4111 879 Pnt 1 g 4240 962 Pnt 1.000 UL LTb @@ -1905,27 +1908,27 @@ LTb 129 -96 V .2258 g 3626 1207 M 258 -74 V -0 g .4839 g 1675 2375 M -.4839 g 1675 2375 M -129 -7 V -.4839 g 1804 2368 M -129 -6 V -.4839 g 1933 2362 M -129 -11 V -.4839 g 2062 2351 M -129 -20 V -.4839 g 2191 2331 M -129 -31 V -.4839 g 2320 2300 M -129 -86 V -.4839 g 2449 2214 M -129 -98 V -.4839 g 2578 2116 M -129 -123 V -.4839 g 2707 1993 M -129 -96 V -.4839 g 2836 1897 M -129 -62 V +0 g .4839 g 1675 2368 M +.4839 g 1675 2368 M +129 -8 V +.4839 g 1804 2360 M +129 12 V +.4839 g 1933 2372 M +129 -12 V +.4839 g 2062 2360 M +129 -9 V +.4839 g 2191 2351 M +129 -49 V +.4839 g 2320 2302 M +129 -84 V +.4839 g 2449 2218 M +129 -107 V +.4839 g 2578 2111 M +129 -115 V +.4839 g 2707 1996 M +129 -69 V +.4839 g 2836 1927 M +129 -92 V .4839 g 2965 1835 M 129 -137 V .4839 g 3094 1698 M @@ -1956,31 +1959,31 @@ LTb 1 g 2434 2193 M 129 -109 V 1 g 2563 2084 M -129 -70 V -1 g 2692 2014 M -129 -129 V -1 g 2821 1885 M -129 26 V -1 g 2950 1911 M -129 -234 V -1 g 3079 1677 M -129 -36 V -1 g 3208 1641 M -129 -116 V -1 g 3337 1525 M -129 -105 V -1 g 3466 1420 M -129 -144 V -1 g 3595 1276 M -129 -90 V -1 g 3724 1186 M -129 -42 V -1 g 3853 1144 M -3982 948 L -1 g 3982 948 M -129 -82 V -1 g 4111 866 M -129 96 V +129 -81 V +1 g 2692 2003 M +129 -91 V +1 g 2821 1912 M +129 -47 V +1 g 2950 1865 M +129 -130 V +1 g 3079 1735 M +129 -76 V +1 g 3208 1659 M +129 -132 V +1 g 3337 1527 M +129 -48 V +1 g 3466 1479 M +129 -176 V +1 g 3595 1303 M +129 -113 V +1 g 3724 1190 M +129 -35 V +1 g 3853 1155 M +3982 975 L +1 g 3982 975 M +129 -96 V +1 g 4111 879 M +129 83 V stroke LTb LCb setrgbcolor diff --git a/fig_metastable.tex b/fig_metastable.tex index 1b757ae..03d36a7 100644 --- a/fig_metastable.tex +++ b/fig_metastable.tex @@ -8,7 +8,7 @@ {\GNUPLOTspecial{" %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 5.2 patchlevel 2 -%%CreationDate: Wed May 9 17:24:16 2018 +%%CreationDate: Thu May 10 20:47:25 2018 %%DocumentFonts: %%BoundingBox: 0 0 246 151 %%EndComments @@ -448,7 +448,7 @@ SDict begin [ /Creator (gnuplot 5.2 patchlevel 2) % /Producer (gnuplot) % /Keywords () - /CreationDate (Wed May 9 17:24:16 2018) + /CreationDate (Thu May 10 20:47:25 2018) /DOCINFO pdfmark end } ifelse diff --git a/monte-carlo.bib b/monte-carlo.bib index 4629ce5..58234c4 100644 --- a/monte-carlo.bib +++ b/monte-carlo.bib @@ -8,7 +8,7 @@ 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.}, + author = {Jose, Jorge V. and Kadanoff, Leo P. and Kirkpatrick, Scott and Nelson, David R.}, month = aug, year = {1977}, pages = {1217--1241}, @@ -420,7 +420,7 @@ number = {22}, urldate = {2018-04-24}, journal = {Physical Review B}, - author = {Manuel Carmona, José and Pelissetto, Andrea and Vicari, Ettore}, + author = {Carmona, Jose Manuel and Pelissetto, Andrea and Vicari, Ettore}, month = jun, year = {2000}, pages = {15136--15151}, @@ -527,4 +527,4 @@ random field Ising model and finally of quantum spin glasses.}, 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} -} \ No newline at end of file +} diff --git a/monte-carlo.pdf b/monte-carlo.pdf index c7ad3f9..f8e5eea 100644 Binary files a/monte-carlo.pdf and b/monte-carlo.pdf differ diff --git a/monte-carlo.tex b/monte-carlo.tex index f88a053..a305aa8 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -130,11 +130,14 @@ algorithms to systems in certain external fields by adding a `ghost site' \cite{coniglio_exact_1989} that returns global rotation invariance to spin Hamiltonians at the cost of an extra degree of freedom, allowing the method to be used in a subcategory of interesting -fields \cite{alexandrowicz_swendsen-wang_1989, destri_swendsen-wang_1992, -lauwers_critical_1989, wang_clusters_1989}. Other categories of fields have +fields \cite{alexandrowicz_swendsen-wang_1989, wang_clusters_1989, ray_metastability_1990}. Static +fields have also been applied by including a separate metropolis or heat bath +update step after cluster formation \cite{destri_swendsen-wang_1992, +lauwers_critical_1989}, and other categories of fields have been applied using replica methods \cite{redner_graphical_1998,chayes_graphical_1998,machta_replica-exchange_2000}. We show that the scaling of -correlation time near the critical point of several models suggests that this +correlation time near the critical point of several models suggests that the +`ghost' approach is a natural one, e.g., that it extends the celebrated scaling of dynamics in these algorithms at zero field to various non-symmetric perturbations. We also show, by a redefinition of the spin--spin coupling in a @@ -390,9 +393,9 @@ represented by a multiplicative group with elements $\{1,-1\}$, exactly the same as the spins themselves. The only nontrivial element is of order two. Since the symmetry group and the spins are described by the same elements, performing the algorithm on the Ising model in a field is fully described by -just using the `ghost spin' representation. This algorithm has been applied -by several researchers \cite{wang_clusters_1989, ray_metastability_1990, -destri_swendsen-wang_1992, lauwers_critical_1989}. +just using the `ghost spin' representation. This algorithm or algorithms +based on the same decomposition of the Hamiltonian have been applied +by several researchers \cite{alexandrowicz_swendsen-wang_1989, wang_clusters_1989, ray_metastability_1990}. \emph{The $\mathrm O(n)$ model.} In the $\mathrm O(n)$ model spins are described by vectors on the $(n-1)$-sphere $S^{n-1}$. Its symmetry group is $O(n)$, $n\times n$ orthogonal diff --git a/prl-paragraph.txt b/prl-paragraph.txt new file mode 100644 index 0000000..754692b --- /dev/null +++ b/prl-paragraph.txt @@ -0,0 +1 @@ +Monte Carlo simulations are important pedagogical and research tools in statistical physics. Cluster methods, like Wolff, continue to be important research tools. This paper takes a method little-known to even those as immersed in the subject as Jon Machta for extending cluster algorithms to operate in a field, generalizes it to a broad class of systems and fields, and makes a quantitative test of its efficiency. This fills an much-needed gap in a canonical method. Fast simulations of the Ising model in a field have been essential in recent work on information geometry, universal scaling of correlation functions, and more. -- cgit v1.2.3-70-g09d2