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-rw-r--r--data/autocorrelation.dat44
-rw-r--r--fig_clusters_ising2d.eps4
-rw-r--r--fig_correlation-temp.tex4
-rw-r--r--fig_correlation.tex4
-rw-r--r--fig_correlation_collapse-hL.tex309
-rw-r--r--fig_metastable.tex4
-rw-r--r--monte-carlo.bib6
-rw-r--r--monte-carlo.pdfbin191228 -> 192821 bytes
-rw-r--r--monte-carlo.tex15
-rw-r--r--prl-paragraph.txt1
10 files changed, 199 insertions, 192 deletions
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
-256 2.26918531421 0.01 1.3931483207074216 0.0864077329366505
-256 2.26918531421 0.0199526 1.2138049242537203 0.0413890164173423
-256 2.26918531421 0.0398107 1.0705826177612325 0.012302212619994533
-256 2.26918531421 0.0794328 0.902218564059897 0
-256 2.26918531421 0.158489 0.8099581184544903 0.008242930678510141
-256 2.26918531421 0.316228 0.7701811359484944 0.06833287459922126
-256 2.26918531421 0.630957 0.609436623797498 0
-256 2.26918531421 1.25893 0.552623201366082 0
+256 2.26918531421 0.000630957 2.1478734963694808 0.04271001425766049
+256 2.26918531421 0.00125893 1.9251797456288635 0.036411621202270004
+256 2.26918531421 0.00251189 1.821483539677408 0.09180025530461666
+256 2.26918531421 0.00501187 1.5598743819132 0.08041405134383199
+256 2.26918531421 0.01 1.4238230988143754 0.047201590428513254
+256 2.26918531421 0.0199526 1.2161313893077417 0.01870141835764084
+256 2.26918531421 0.0398107 1.1492259267242733 0.07685234754577898
+256 2.26918531421 0.0794328 0.9311090143123605 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 @@
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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 @@
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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{"
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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 @@
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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{"
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} 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
--- a/monte-carlo.pdf
+++ b/monte-carlo.pdf
Binary files 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.