English
Related papers

Related papers: The Random-bond Potts model in the large-q limit

200 papers

We review recent investigations of the critical behavior of ferromagnetic $q$-state Potts models on a class of hierarchical lattices, with exchange interactions according to some deterministic but aperiodic substitution rules. The problem…

Statistical Mechanics · Physics 2007-05-23 T. A. S. Haddad , S. T. R. Pinho , S. R. Salinas

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up…

Statistical Mechanics · Physics 2021-01-01 Sabino José Ferreira , Alan D. Sokal

In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their…

Statistical Mechanics · Physics 2009-07-23 Márton Karsai

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we…

Statistical Mechanics · Physics 2024-06-26 M. P. Qin , J. Chen , Q. N. Chen , Z. Y. Xie , X. Kong , H. H. Zhao , B. Normand , T. Xiang

We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1…

Computational Complexity · Computer Science 2012-11-13 Leslie Ann Goldberg , Mark Jerrum

The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…

Statistical Mechanics · Physics 2009-11-07 Zvonko Glumac , Katarina Uzelac

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and…

Disordered Systems and Neural Networks · Physics 2020-12-29 Utkarsh Agrawal , Sarang Gopalakrishnan , Romain Vasseur

We present results of a numerical simulation of the $q$-state random bond Potts model in two dimensions and for large $q$. In particular, care is taken to study the crossover from the pure model to the random model, as well as the crossover…

Statistical Mechanics · Physics 2007-05-23 Marco Picco

We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values…

Statistical Mechanics · Physics 2015-10-28 Shu-Chiuan Chang , Robert Shrock

We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply,…

Data Structures and Algorithms · Computer Science 2020-03-25 Matthew Jenssen , Peter Keevash , Will Perkins

We show that large deviation properties of Erd\"os-R\'enyi random graphs can be derived from the free energy of the $q$-state Potts model of statistical mechanics. More precisely the Legendre transform of the Potts free energy with respect…

Statistical Mechanics · Physics 2009-11-10 Andreas Engel , Rémi Monasson , Alexander K. Hartmann

We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in…

Disordered Systems and Neural Networks · Physics 2009-11-07 Christophe Chatelain , Bertrand Berche , Lev N. Shchur

We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self--dual…

Statistical Mechanics · Physics 2007-05-23 Lincoln Chayes , Kirill Shtengel

The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…

Statistical Mechanics · Physics 2013-07-16 M. Krasnytska , B. Berche , Yu. Holovatch

Boundary critical phenomena are studied in the 3- State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and…

Condensed Matter · Physics 2009-10-31 Ian Affleck , Masaki Oshikawa , Hubert Saleur

We review and extend some recent investigations of the effects of aperiodic interactions on the critical behavior of ferromagnetic $q$-state Potts models. By considering suitable diamond or necklace hierarchical lattices, and assuming a…

Statistical Mechanics · Physics 2009-11-07 T. A. S. Haddad , S. R. Salinas

In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…

Combinatorics · Mathematics 2014-08-27 L. Beaudin , J. Ellis-Monaghan , G. Pangborn , R. Shrock

We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge…

Probability · Mathematics 2023-02-28 Antonio Blanca , Reza Gheissari

It is known that a trained Restricted Boltzmann Machine (RBM) on the binary Monte Carlo Ising spin configurations, generates a series of iterative reconstructed spin configurations which spontaneously flow and stabilize to the critical…

Disordered Systems and Neural Networks · Physics 2022-05-11 Dimitrios Giataganas , Ching-Yu Huang , Feng-Li Lin

The $Q$-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on…

Statistical Mechanics · Physics 2015-06-24 Seung-Yeon Kim