English
Related papers

Related papers: Partition function zeros of the Q-state Potts mode…

200 papers

We study properties of the Potts model partition function $Z(H_m,q,v)$ on $m$'th iterates of Hanoi graphs, $H_m$, and use the results to draw inferences about the $m \to \infty$ limit that yields a self-similar Hanoi fractal, $H_\infty$. We…

Statistical Mechanics · Physics 2025-02-05 Shu-Chiuan Chang , Robert Shrock

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are…

Condensed Matter · Physics 2014-10-13 Victor Matveev , Robert Shrock

Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on non-periodic systems based on substitution. In…

Statistical Mechanics · Physics 2007-05-23 Harald Simon , Michael Baake , Uwe Grimm

To simulate indistinguishable particles, recent studies of path-integral molecular dynamics formulated their partition function $Z$ as a recurrence relation involving a variable $\xi$, with $\xi=1$(-1) for bosons (fermions). Inspired by…

Statistical Mechanics · Physics 2026-02-27 Ran-Chen He , Jia-Xi Zeng , Shu Yang , Cong Wang , Qi-Jun Ye , Xin-Zheng Li

The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…

High Energy Physics - Lattice · Physics 2011-07-19 A J Guttmann , I G Enting

The density of the Fisher zeroes, or zeroes of the partition function in the complex temperature plane, is determined for the Ising model in zero field as well as in a pure imaginary field i Pi/2. Results are given for the simple-quartic,…

Statistical Mechanics · Physics 2015-06-24 Wentao T. Lu , F. Y. Wu

Partition function zeros steer the critical behavior of a system. Studying four-flavor lattice QCD at finite temperature and density with the Wilson-clover fermion action and the Iwasaki gauge action using a phase-quenched fermion…

High Energy Physics - Lattice · Physics 2013-11-18 Xiao-Yong Jin , Yoshinobu Kuramashi , Yoshifumi Nakamura , Shinji Takeda , Akira Ukawa

partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of…

We present a set of general results on structural features of the $q$-state Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature Boltzmann variable $v$ for various lattice strips of arbitrarily great width $L_y$…

Statistical Mechanics · Physics 2009-11-07 Shu-Chiuan Chang , Robert Shrock

We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer…

Disordered Systems and Neural Networks · Physics 2008-08-04 Yoshiki Matsuda , Hidetoshi Nishimori , Koji Hukushima

We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…

Mathematical Physics · Physics 2019-08-14 Paolo Lorenzoni , Antonio Moro

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on self-dual strip graphs $G$ of the square lattice with fixed width $L_y$ and arbitrarily great length $L_x$…

Statistical Mechanics · Physics 2009-11-07 Shu-Chiuan Chang , Robert Shrock

The lowest zeros of the lattice partition function for non-compact QED are found in the complex fermion mass plane on $6^4$, $8^4$ and $10^4$ lattices at intermediate values of the coupling. The scaling of the low lying zeros with lattice…

High Energy Physics - Lattice · Physics 2009-10-28 A. Ali Khan , I. Barbour

The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model…

Statistical Mechanics · Physics 2007-05-23 Richard J. Creswick , Seung-Yeon Kim

We study the thermodynamic singularities of QCD in the complex chemical potential plane by a numerical simulation of lattice QCD, and discuss a method to understand the nature of the QCD phase transition at finite density from the…

High Energy Physics - Lattice · Physics 2010-02-19 Shinji Ejiri , Hiroshi Yoneyama

We present exact calculations of the zero-temperature partition function (chromatic polynomial) $P$ for the $q$-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length $L_x$ vertices and of width $L_y=3$…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for…

Statistical Mechanics · Physics 2015-06-24 Shu-Chiuan Chang , Jesper Lykke Jacobsen , Jesús Salas , Robert Shrock

We prove that for the Ising model on a lattice of dimensionality $d \ge 2$, the zeros of the partition function $Z$ in the complex $\mu$ plane (where $\mu=e^{-2\beta H}$) lie on the unit circle $|\mu|=1$ for a wider range of $K_{n n'}=\beta…

Condensed Matter · Physics 2009-10-28 Victor Matveev , Robert Shrock

By setting the inverse temperature $\beta$ loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $\beta$ axis, reveal a thermodynamic phase transition. More recently,…

Strongly Correlated Electrons · Physics 2025-01-17 Yang Liu , Songtai Lv , Yuchen Meng , Zefan Tan , Erhai Zhao , Haiyuan Zou