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We present a new method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the single electron…

Statistical Mechanics · Physics 2026-01-14 B Sriram Shastry

In this paper, we study the $n$-point function of $t$-core partitions. The main tool is the topological vertex, originally developed to study the topological string theory for toric Calabi--Yau 3-folds. By virtue of the topological vertex,…

Mathematical Physics · Physics 2026-04-17 Chenglang Yang

We apply harmonic analysis to study the $T\bar{T}$-deformed torus partition function. We first express the CFT partition functions in terms of Maass waveforms, including the Eisenstein series and cusp forms. These basis functions turn out…

High Energy Physics - Theory · Physics 2026-05-06 Jie Gu , Jue Hou , Yunfeng Jiang

In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of the model in the thermodynamic limit. We consider the same…

Mathematical Physics · Physics 2015-05-13 A. V. Razumov , Yu. G. Stroganov

Worldsheet (0,2) gauged linear sigma models are often used to study supersymmetric heterotic string compactifications with non-trivial vector bundles. We make use of supersymmetric localization techniques to determine their one-loop…

High Energy Physics - Theory · Physics 2014-08-28 Stefan Groot Nibbelink , Fabian Ruehle

We continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified…

Mathematical Physics · Physics 2026-03-11 Matthieu Cornillault , Samuel Belliard

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site…

Mathematical Physics · Physics 2013-11-19 M. Assis , J. L. Jacobsen , I. Jensen , J-M. Maillard , B. M. McCoy

The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…

Mathematical Physics · Physics 2009-10-31 P. Zinn-Justin

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures.…

Strongly Correlated Electrons · Physics 2009-11-07 M. A. Martin-Delgado , M. Roncaglia , G. Sierra

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for…

Mathematical Physics · Physics 2009-11-10 Christian Korff

Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…

Strongly Correlated Electrons · Physics 2019-03-27 Jie Wang , Scott D. Geraedts , E. H. Rezayi , F. D. M. Haldane

We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy…

Statistical Mechanics · Physics 2015-03-17 Jae Hwan Lee , Seung-Yeon Kim , Julian Lee

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

A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…

General Physics · Physics 2013-10-02 C. B. Yang

This paper gives an exposition of well known results on vector partition functions. The exposition is based on works of M. Brion, A. Szenes and M. Vergne and is geared toward explicit computer realizations. In particular, the paper presents…

Representation Theory · Mathematics 2010-11-25 Todor Milev

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 square-lattice strip graphs $G$ for a variety of transverse widths $L_t$ and for arbitrarily…

Statistical Mechanics · Physics 2015-10-08 Jesus Salas , Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder graphs with free, cyclic, and M\"obius…

Statistical Mechanics · Physics 2009-10-31 Robert Shrock

The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…

Statistical Mechanics · Physics 2019-04-26 Bo-Yuan Ning , Le-Cheng Gong , Tsu-Chien Weng , Xi-Jing Ning

In this paper we implement a numerical algorithm to compute codimension-one tori in three-dimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The…

Chaotic Dynamics · Physics 2013-10-01 Adam M. Fox , James D. Meiss

We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…

Machine Learning · Computer Science 2012-06-18 Arthur Choi , Adnan Darwiche