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Related papers: Partition function zeros of aperiodic Ising models

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In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and…

Statistical Mechanics · Physics 2015-06-22 Julian Lee

We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…

Mathematical Physics · Physics 2007-05-23 Marek Biskup , Christian Borgs , Jennifer T. Chayes , Logan J. Kleinwaks , Roman Kotecky

We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched…

Condensed Matter · Physics 2009-10-22 P. H. Damgaard , J. Lacki

The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of…

Statistical Mechanics · Physics 2010-06-03 G. Nandhini , M. Vinoth Kumar , M. V. Sangaranarayanan

The seminal Lee-Yang theorem states that for any graph the zeros of the partition function of the ferromagnetic Ising model lie on the unit circle in $\mathbb C$. In fact the union of the zeros of all graphs is dense on the unit circle. In…

Combinatorics · Mathematics 2022-03-01 Han Peters , Guus Regts

Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…

Statistical Mechanics · Physics 2011-11-28 R. K. Bhaduri , A. MacDonald , W. van Dijk

We consider the Ising model on an $M\times N$ rectangular lattice with an asymmetric self-dual boundary condition, and derive a closed-form expression for its partition function. We show that zeroes of the partition function are given by…

Statistical Mechanics · Physics 2009-10-31 Wentao T. Lu , F. Y. Wu

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

Fisher zeros play a central role in the theoretical understanding of phase transitions. However, their computation requires knowledge of the density of states, which limits their practical applicability. Alternative approaches based on the…

Computational Physics · Physics 2026-05-22 R. G. M. Rodrigues

We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising Model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the…

Dynamical Systems · Mathematics 2021-07-01 Ferenc Bencs , Pjotr Buys , Lorenzo Guerini , Han Peters

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…

Quantum Physics · Physics 2019-07-12 Ryan L. Mann , Michael J. Bremner

We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and…

Statistical Mechanics · Physics 2024-10-16 Denis Gessert , Martin Weigel , Wolfhard Janke

Low-temperature expansion of Ising model has long been a topic of significant interest in condensed matter and statistical physics. In this paper we present new results of the coefficients in the low-temperature series of the Ising…

Statistical Mechanics · Physics 2025-10-16 De-Zhang Li , Xin Wang , Xiao-Bao Yang

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in…

Condensed Matter · Physics 2009-11-10 Natali Gulbahce , Harvey Gould , W. Klein

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

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 extend the renormalization group transformation based on the two-lattice matching to the complex inverse temperature plane for Dyson's hierarchical Ising model. We consider values of the dimensional parameter above, below and exactly at…

High Energy Physics - Lattice · Physics 2011-06-02 Yuzhi Liu , Y. Meurice

This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of…

Mathematical Physics · Physics 2007-05-23 Marek Biskup , Christian Borgs , Jennifer T. Chayes , Roman Kotecky

We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high- and…

High Energy Physics - Lattice · Physics 2015-06-25 W. Janke , D. Johnston , M. Stathakopoulos

We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T=0 in the…

Condensed Matter · Physics 2009-10-31 R. Burioni , D. Cassi , L. Donetti