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Related papers: Comment on ``Antiferromagnetic Potts Models''

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Given an infinite graph $\GI$ quasi-transitive and amenable with maximum degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$ of the q-state antiferromagnetic Potts model at zero temperature on $\GI$ is analytic…

Statistical Mechanics · Physics 2009-11-07 Aldo Procacci , Benedetto Scoppola , Victor Gerasimov

We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More…

Mathematical Physics · Physics 2014-09-18 Roman Kotecký , Alan D. Sokal , Jan M. Swart

The low-temperature series are calculated for the free energy, magnetization and susceptibility in the Q-state Potts model on the square lattice, using the improved algorithm of the finite lattice method. The series are obtained to the…

Condensed Matter · Physics 2009-10-30 H. Arisue , K. Tabata

We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…

Statistical Mechanics · Physics 2007-05-23 S. Grollau , M. L. Rosinberg , G. Tarjus

We study the $q$ states Potts model with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q\leq 4$ the system exhibits a second-order phase transition, and when $q >…

Statistical Mechanics · Physics 2018-03-14 Nir Schreiber , Reuven Cohen , Simi Haber

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using Monte Carlo simulations. The ordering in a medium temperature range below the critical point is investigated in detail. Two different regimes have…

Condensed Matter · Physics 2009-10-28 M. Kolesik , M. Suzuki

The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN…

High Energy Physics - Lattice · Physics 2026-03-26 Shang-Wei Li , Kai-Wei Huang , Chien-Ting Chen , Fu-Jiun Jiang

We provide a new criterion based on graph duality to predict whether the 3-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for…

Statistical Mechanics · Physics 2018-05-09 Jian-Ping Lv , Youjin Deng , Jesper Lykke Jacobsen , Jesús Salas , Alan D. Sokal

We present exact calculations of the zero-temperature partition function, $Z(G,q,T=0)$, and ground-state degeneracy (per site), $W({G},q)$, for the $q$-state Potts antiferromagnet on a number of families of graphs ${G}$ for which the…

Statistical Mechanics · Physics 2009-10-31 Robert Shrock , Shan-Ho Tsai

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero…

Statistical Mechanics · Physics 2021-01-01 John Cardy , Jesper Lykke Jacobsen , Alan D. Sokal

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times…

Statistical Mechanics · Physics 2009-11-07 Jesus Salas , Robert Shrock

We have studied the ordering of the q-colours Potts model in two dimensions on a square lattice. On the basis of our observations we propose that if q is large enough the system is not able to break global and local null magnetisation…

Statistical Mechanics · Physics 2007-05-23 Miguel Ibanez de Berganza , Vittorio Loreto , Alberto Petri

We prove the existence of long-range order for the 3-state Potts antiferromagnet at low temperature on $\mathbb{Z}^d$ for sufficiently large $d$. In particular, we show the existence of six extremal and ergodic infinite-volume Gibbs…

Mathematical Physics · Physics 2017-08-29 Ohad Feldheim , Yinon Spinka

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le8$), no Fisher…

Statistical Mechanics · Physics 2009-10-31 Seung-Yeon Kim , Richard J. Creswick , Chi-Ning Chen , Chin-Kun Hu

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the…

Statistical Mechanics · Physics 2009-10-31 H. Feldmann , A. J. Guttmann , I , Jensen , R. Shrock , S. -H. Tsai

We solve the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic) on the square lattice. The solution is based on a detailed analysis of the Bethe ansatz equations (which involve staggered source…

Statistical Mechanics · Physics 2008-11-26 Jesper Lykke Jacobsen , Hubert Saleur

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). HOTRG works in the thermodynamic limit, where we…

Statistical Mechanics · Physics 2014-09-16 S. Wang , Z. Y. Xie , J. Chen , B. Normand , T. Xiang

We present exact calculations of the zero-temperature partition function for the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices…

Statistical Mechanics · Physics 2009-10-31 S. -C. Chang , R. Shrock

We study the four-state antiferromagnetic Potts model on the triangular lattice. We show that the model has six types of defects which diffuse and annihilate according to certain conservation laws consistent with their having a…

Statistical Mechanics · Physics 2007-05-23 Cristopher Moore , M. E. J. Newman

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