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Monte Carlo Methods for the Ferromagnetic Potts Model Using Factor Graph Duality [article]

Mehdi Molkaraie, Vicenc Gomez
2018 arXiv   pre-print
Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models.  ...  Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo methods, which are known to work well at high temperatures, but to  ...  The first author thanks these institutions for hospitality and support.  ... 
arXiv:1506.07044v4 fatcat:frz3gwzvwnbwpmpg6rvevyi6wy

Monte Carlo Methods for the Ferromagnetic Potts Model Using Factor Graph Duality

Mehdi Molkaraie, Vicenc Gomez
2018 IEEE Transactions on Information Theory  
Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models.  ...  Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo methods, which are known to work well at high temperatures, but to  ...  The first author thanks these institutions for hospitality and support.  ... 
doi:10.1109/tit.2018.2857565 fatcat:iglrt57st5at3fha5aux62b64e

An Importance Sampling Scheme on Dual Factor Graphs. I. Models in a Strong External Field [article]

Mehdi Molkaraie
2015 arXiv   pre-print
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic q-state Potts model, both in the presence  ...  The proposed scheme operates in the dual Forney factor graph and is capable of efficiently computing an estimate of the partition function under a wide range of model parameters.  ...  ACKNOWLEDGEMENTS The author would like to thank Hans-Andrea Loeliger, Pascal Vontobel, and Justin Dauwels for their comments that greatly improved the presentation of this paper.  ... 
arXiv:1401.4912v5 fatcat:aqzbnyb22rg4zbofj2pbfjmumi

An importance sampling scheme for models in a strong external field

Mehdi Molkaraie
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
We propose Monte Carlo methods to estimate the partition function of the two-dimensional Ising model in the presence of an external magnetic field.  ...  The estimation is done in the dual of the Forney factor graph representing the model.  ...  Dual Forney factor graphs and the factor graph duality theorem are discussed in Section III. The proposed Monte Carlo methods are described in Section IV.  ... 
doi:10.1109/isit.2015.7282641 dblp:conf/isit/Molkaraie15 fatcat:isxg5mh5yfd6xm27sp3uborzei

Parallel-tempering cluster algorithm for computer simulations of critical phenomena

Elmar Bittner, Wolfhard Janke
2011 Physical Review E  
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point.  ...  As a result, we gain one to two orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic  ...  The non-equilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations [2] .  ... 
doi:10.1103/physreve.84.036701 pmid:22060523 fatcat:phxvsva77jexzjzmzl6j4uxxd4

Marginal Densities, Factor Graph Duality, and High-Temperature Series Expansions [article]

Mehdi Molkaraie
2020 arXiv   pre-print
in the dual normal factor graph of the model.  ...  Details of the mapping, including its fixed points, are derived for the Ising model, and then extended to the Potts model.  ...  Acknowledgements The author is extremely grateful to G. D. Forney, Jr., for his comments and for his continued support. The author also wishes to thank J. Dauwels, P. Vontobel, V. Gómez, and B.  ... 
arXiv:1901.02733v3 fatcat:4lpt6pzlebcarbgewhvnwcge4q

Page 829 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
This model has already been studied by series expansion and Monte Carlo methods with inconclusive results.  ...  Thus it is a generalisation of the eight-vertex model on the plane square lattice and we can apply the weak graph transformation to obtain a duality relation for the model.  ... 

Triangular lattice Potts models

I. G. Enting, F. Y. Wu
1982 Journal of statistical physics  
In this paper we study the 3-state Potts model on the triangular lattice which has two-and three-site interactions.  ...  KEY WORDS: Potts model; triangular lattice; Peierls argument; lowtemperature series; phase diagram; relations with other lattice models. Triangular Lattice Potts Models 3?  ...  ACKNOWLEDGMENTS One of us (F.Y.W.) wishes to express his thanks to P. W. Kasteleyn and J. M. J. van Leeuwen for the kind hospitality extended to him at the  ... 
doi:10.1007/bf01012610 fatcat:aubhfhdr2zhvbbnzcaxh6q4pty

An Importance Sampling Algorithm for the Ising Model with Strong Couplings [article]

Mehdi Molkaraie
2017 arXiv   pre-print
The estimation is done via importance sampling in the dual of the Forney factor graph representing the model.  ...  We consider the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field.  ...  The author would also like to thank Pascal Vontobel for proofreading an earlier version of this paper and for pointing out to him [19] .  ... 
arXiv:1404.5666v7 fatcat:jj23v7yhmjhopnayt45wlxrylq

Phase diagram of the two-dimensional ferromagnetic three-color Ashkin–Teller model

F.A.P. Piolho, F.A. da Costa, C.G. Bezerra, A.M. Mariz
2008 Physica A: Statistical Mechanics and its Applications  
Our numerical results show the presence of four universality classes, three of them are associated to the Potts model with q = 2, 4 and 6 states.  ...  In the present work we study the critical properties of the ferromagnetic three-color Ashkin-Teller model (3AT) by means of a Migdal-Kadanoff renormalization group approach on a diamond-like hierarchical  ...  Queiroz for fruitful discussions. We are in debt to Dr. A.O. Sousa for a critical reading of the manuscript.  ... 
doi:10.1016/j.physa.2007.11.009 fatcat:g7nr5ygrz5evtaarigf5ojnbmu

A challenge in enumerative combinatorics: The graph of contribution [article]

J-M.Maillard
2002 arXiv   pre-print
Wu's most important and well-known classic results and we will also sketch his most recent researches dedicated to the connections of lattice statistical mechanical models with deep problems in pure mathematics  ...  Wu's contributions in lattice statistical mechanics, solid state physics, graph theory, enumerative combinatorics and so many other domains of physics and mathematics. We will recall F. Y.  ...  I would also like to thank Fred for so many passionate discussions on lattice models throughout the years. I would like to thank A. J.  ... 
arXiv:cond-mat/0205063v2 fatcat:jeeghzq2hncmhkthwkysyrntni

Phase diagram for the Ashkin-Teller model in three dimensions

Ruth V. Ditzian, Jayanth R. Banavar, G. S. Grest, Leo P. Kadanoff
1980 Physical Review B (Condensed Matter)  
Highand low-temperature series, Monte Carlo simulations, mean-field calculations, and renormalization-group ideas are used to analyze the behavior of the Ashkin-Teller model in three dimensions.  ...  The data generated by series and Monte Carlo methods in the neighborhood of the decoupling point are consistent with the renormalization-group conclusion that this system cannot show a line of continuously  ...  The technique for obtaining and analyzing the series and a brief description of the Monte Carlo method are described in the Appendixes.  ... 
doi:10.1103/physrevb.22.2542 fatcat:kbkzrb3a7vc3bpx54cvnntvnji

The anisotropic Ashkin–Teller model: a renormalization group study

C.G. Bezerra, A.M. Mariz, J.M. de Araújo, F.A. da Costa
2001 Physica A: Statistical Mechanics and its Applications  
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach.  ...  The critical frontier, separating five distinct phases, recover all the known exacts results for the square lattice.  ...  Acknowledgments We are grateful to CNPq and Pronex/MCT (Brazilian research funding foundations) for partial financial support.  ... 
doi:10.1016/s0378-4371(00)00568-9 fatcat:udmumy6jcbgixjwugba7keqlay

Critical manifold of the kagome-lattice Potts model

Jesper Lykke Jacobsen, Christian R Scullard
2012 Journal of Physics A: Mathematical and Theoretical  
We illustrate the method for the square lattice, where the Potts model has been exactly solved, and the kagome lattice, where it has not.  ...  In this sense, the computation of P_B(q,v) can be used to detect exact solvability of the Potts model on G.  ...  JLJ wishes to express his gratitude to Jesús Salas for collaboration on a related project [21] . Both authors thank J. Salas and F.Y. Wu for some interesting comments on the manuscript.  ... 
doi:10.1088/1751-8113/45/49/494003 fatcat:u5qv6kfklbc67gqgenbwlq3txy

High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials

Masayuki Ohzeki, Jesper Lykke Jacobsen
2015 Journal of Physics A: Mathematical and Theoretical  
We apply the method to obtain the phase diagrams of the random-bond Ising model and q-state Potts gauge glasses.  ...  We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses.  ...  Acknowledgments The authors are grateful for the fruitful discussions with Koji Hukushima, Ryoji Miyazaki, Christian R. Scullard, and Koujin Takeda.  ... 
doi:10.1088/1751-8113/48/9/095001 fatcat:bexov45jxbe7jkdpzb6z6i7n7m
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