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A new approach to Monte Carlo simulations in statistical physics

D. P. Landau, F. Wang
2004 Brazilian journal of physics  
Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to directly extract an estimate for the density of states.  ...  We describe a new algorithm that approaches Monte Carlo simulation in statistical physics in a different way.  ...  Acknowledgments This research has been supported by the National Science Foundation under Grant No. DMR-0094422.  ... 
doi:10.1590/s0103-97332004000300004 fatcat:u6j6atbltbbbza2zewymhf7gia

Rotationally symmetric ordered phase in the three-state antiferromagnetic Potts model

Ralf K. Heilmann, Jian-Sheng Wang, Robert H. Swendsen
1996 Physical Review B (Condensed Matter)  
We investigate the three-state antiferromagnetic Potts model on a simple cubic lattice with a cluster flipping Monte Carlo simulation algorithm in the temperature region below the transition into disorder  ...  We find both the well established broken-sublattice-symmetry (BSS) phase at low temperature and a new, rotationally symmetric phase at higher temperature, but below T_c1.  ...  At a temperature of T c1 = 1.22605(5) as determined by earlier Monte Carlo studies 4 the model undergoes an order-disorder phase transition, belonging to the XY model universality class.  ... 
doi:10.1103/physrevb.53.2210 pmid:9983712 fatcat:y4xie6evrfew5kyf55coom6g54

Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

Shun Wang, Zhi-Yuan Xie, Jing Chen, Bruce Normand, Tao Xiang
2014 Chinese Physics Letters  
Our results verify the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.  ...  We investigate the 2- and 3-state ferromagnetic Potts models on the simple cubic lattice using the tensor renormalization group method with higher-order singular value decomposition (HOTRG).  ...  II Comparison of latent heats ∆E and transition temperatures Tc for the q = 3 ferromagnetic Potts model on the simple cubic lattice obtained by different methods.  ... 
doi:10.1088/0256-307x/31/7/070503 fatcat:afrzbn62bzagfkirrkvhkohiqi

Application of the exchange Monte Carlo method to ordering dynamics

Yutaka Okabe
1999 New Journal of Physics  
Even for the deeply quenched case to low temperatures, we have observed a rapid domain growth; we have proved the efficiency of the exchange Monte Carlo method for the ordering process.  ...  We apply the exchange Monte Carlo method to the ordering dynamics of the three-state Potts model with the conserved order parameter.  ...  The computation in this work was carried out using the facilities of the Supercomputer Center, Institute for Solid State Physics, University of Tokyo.  ... 
doi:10.1088/1367-2630/1/1/310 fatcat:2k4vtoakbretlb47tqy6lzderi

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

Mehdi Molkaraie, Vicenc Gomez
2018 arXiv   pre-print
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  ...  fail at low temperatures.  ...  Part of this work was done during the first author's stay at the Institut Henri Poincaré -Centre Emile Borel, France, at the Information Theory and Coding Group, University of Pompeu Fabra, Spain, and  ... 
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  
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  ...  fail at low temperatures.  ...  Part of this work was done during the first author's stay at the Institut Henri Poincaré -Centre Emile Borel, France, at the Information Theory and Coding Group, University of Pompeu Fabra, Spain, and  ... 
doi:10.1109/tit.2018.2857565 fatcat:iglrt57st5at3fha5aux62b64e

Monte Carlo study of the antiferromagnetic three-state Potts model with a staggered polarization field on the square lattice

Yutaka Okabe, Hiromi Otsuka
2006 Journal of Physics A: Mathematical and General  
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice.  ...  We obtain two phase transitions; one belongs to the ferromagnetic three-state Potts universality class, and the other to the Ising universality class.  ...  This work was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.  ... 
doi:10.1088/0305-4470/39/29/006 fatcat:b6cdg4sx2zg7tlcxyhsnirww5u

Efficient parallel tempering for first-order phase transitions

T. Neuhaus, M. P. Magiera, U. H. E. Hansmann
2007 Physical Review E  
We present a Monte Carlo algorithm that facilitates efficient parallel tempering simulations of the density of states g͑E͒.  ...  We show that the algorithm eliminates the supercritical slowing down in the case of the Q = 20 and Q = 256 Potts models in two dimensions, typical examples for systems with extreme first-order phase transitions  ...  The total Monte Carlo statistics is 0.5ϫ 10 9 V local spin updates for given box sizes L Յ 64 at volume V = L 2 .  ... 
doi:10.1103/physreve.76.045701 pmid:17995052 fatcat:h6zaiaz3sbbaxo5wjd2mp7upb4

Inverse renormalization group based on image super-resolution using deep convolutional networks

Kenta Shiina, Hiroyuki Mori, Yusuke Tomita, Hwee Kuan Lee, Yutaka Okabe
2021 Scientific Reports  
We consider the improved correlation configuration instead of spin configuration for the spin models, such as the two-dimensional Ising and three-state Potts models.  ...  In the framework of the dual Monte Carlo algorithm, the block-cluster transformation is regarded as a transformation in the graph degrees of freedom, whereas the block-spin transformation is that in the  ...  Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science, Grant Number, JP19K03657.  ... 
doi:10.1038/s41598-021-88605-w pmid:33953229 fatcat:rlxtdqksubhulkhk2xr47wrtvi

Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram

Fugao Wang, D. P. Landau
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models.  ...  We obtained direct simulational estimates for the density of states for two-dimensional ten-state Potts models on lattices up to 200 × 200 and Ising models on lattices up to 256 × 256.  ...  at any temperature without performing multiple simulations. at the transition temperature T c t for the first-order transition of the Q d C 10 Potts model.  ... 
doi:10.1103/physreve.64.056101 pmid:11736008 fatcat:3o7wvzl665adfkw24iy7q3g35y

Monte Carlo Simulation of Grain Growth

Yoshiyuki Saito, Masato Enomoto
1992 ISIJ International  
The conversion of Monte Carlo step to real time is attempted based on diffusion controlled mechanisms.The estimated grain size with use of the conversion formula in pure iron at 1 273 K is in good agreement  ...  The nearest neighbor sides correlation like Aboav-Weaire relation is observed in both grain structures computedby Potts model and modified Potts model.  ...  Monte Carlo computer simulation technique proposed by Exxon group (Potts model)35) is one of the most promising methods to detailed informatlon on the topology and kinetics of microstructure evolution.  ... 
doi:10.2355/isijinternational.32.267 fatcat:hnrpx4wiazbelkb3ri2k6jklxu

A fast serial algorithm for the finite temperature quenched Potts model

G. N. Hassold, Elizabeth A. Holm
1993 Computers in physics  
Srolovitz for valuable discussions.  ...  ACKNOWLEDGMENTS GNH thanks GMI for support under a research initiation grant.  ...  Although the efficiencies of simulations at low temperatures (kT /E 0 ..;0.3 or T<TJ2) are very similar, simulations at higher temperatures are much less efficient.  ... 
doi:10.1063/1.168481 fatcat:briqcp43vvdgtiahaeejdukqei

A Neural Networks study of the phase transitions of Potts model [article]

D.-R. Tan, C.-D. Li, W.-P. Zhu, F.-J. Jiang
2019 arXiv   pre-print
two channels, determined by the NN method is as strong as that calculated with the Monte Carlo technique.  ...  Remarkably, our investigation of these two models provides convincing evidence for the effectiveness of the method of preparing training sets used in this study.  ...  Monte Carlo system may not be applicable for this model.  ... 
arXiv:1912.12042v1 fatcat:wg2adc56evgphf7iaryhyobwba

Equilibrating Glassy Systems with Parallel Tempering [article]

Walter Kob, Claudio Brangian, Torsten Stuhn, Ryoichi Yamamoto
2000 arXiv   pre-print
We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures.  ...  , at low temperatures, new independent configurations at a rate which is O(100) times faster than more traditional algorithms, such as molecular dynamics and single spin flip Monte Carlo dynamics.  ...  Figure 8 : 8 Spin-autocorrelation function for the fully connected Potts-glass (q = 10) as obtained from the PT algorithm and the standard single spin flip Monte Carlo Method.  ... 
arXiv:cond-mat/0003282v1 fatcat:r3luh5z5xrcbbjszdvpfvycr4y

Hybrid multicanonical cluster algorithm for efficient simulations of long-range spin models

S. Reynal, H.T. Diep
2005 Computer Physics Communications  
An efficient, flat histogram Monte Carlo algorithm is proposed that simulates long-range spin models in the multicanonical ensemble with very low dynamic exponents and drastically reduced computational  ...  Numerical results demonstrate the remarkable performance of the method over a wide spectrum of model parameters.  ...  INTRODUCTION Amidst powerful methods dedicated to the study of longrange spin models, Monte Carlo (MC) methods have now gained a prominent role [1, 2, 3, 4] .  ... 
doi:10.1016/j.cpc.2005.03.056 fatcat:tehbg3iomvfsphglknfhys6nmy
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