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In a classical work of the 1950's, Lee and Yang proved that the zeros of the partition functions of a ferromagnetic Ising models always lie on the unit circle. Distribution of these zeros is physically important as it controls phase…

Dynamical Systems · Mathematics 2010-09-24 Pavel Bleher , Mikhail Lyubich , Roland Roeder

We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as $P(k)\sim…

Statistical Mechanics · Physics 2016-03-23 M. Krasnytska , B. Berche , Yu. Holovatch , R. Kenna

The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…

Condensed Matter · Physics 2015-06-25 M. Baake , U. Grimm , C. Pisani

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

The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition…

Statistical Mechanics · Physics 2007-05-23 R. G. Ghulghazaryan , N. S. Ananikian

The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the…

Disordered Systems and Neural Networks · Physics 2025-03-14 Chaoming Song

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

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

A general analytical formula for recurrence relations of multisite interaction Ising models in an external magnetic field on the Cayley-type lattices is derived. Using the theory of complex analytical dynamics on the Riemann sphere, a…

Statistical Mechanics · Physics 2009-10-31 N. S. Ananikian , R. G. Ghulghazaryan

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations have confirmed that the free energy of QCD is a quartic function of quark chemical potential at…

High Energy Physics - Lattice · Physics 2015-05-27 Keitaro Nagata , Kouji Kashiwa , Atsushi Nakamura , Shinsuke M. Nishigaki

Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent…

Statistical Mechanics · Physics 2022-12-14 Chengshu Li , Fan Yang

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

Lee-Yang zeros are points on the complex plane of magnetic field where the partition function of a spin system is zero and therefore the free energy diverges. Lee-Yang zeros and their generalizations are ubiquitous in many-body systems and…

Quantum Physics · Physics 2015-01-08 Xinhua Peng , Hui Zhou , Bo-Bo Wei , Jiangyu Cui , Jiangfeng Du , Ren-Bao Liu

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 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

Lee-Yang zeros are points in the complex plane of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on…

Mesoscale and Nanoscale Physics · Physics 2019-09-06 Aydin Deger , Christian Flindt

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

The Lee-Yang property of a given spin model means that its partition function has purely imaginary zeros as a function of an external magnetic field. A similar property is also used in the theory of quantum anharmonic crystals and quantum…

Mathematical Physics · Physics 2026-03-20 Yuri Kozitsky

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems.…

Mesoscale and Nanoscale Physics · Physics 2018-01-17 Aydin Deger , Kay Brandner , Christian Flindt

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 low…

Statistical Mechanics · Physics 2009-11-07 W. Janke , D. A. Johnston , M. Stathakopoulos
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