Exact low-temperature series expansion for the partition function of the two-dimensional zero-field s=1/2 Ising model on the infinite square lattice

TL;DR

This paper derives exact low-temperature series coefficients for the 2D Ising model's partition function, revealing insights into phase transition mechanisms via a combinatorial approach applicable to various lattice models.

Contribution

It provides the exact coefficients for the low-temperature series expansion of the 2D Ising model, linking phase transition behavior to a gas of energy clusters model.

Findings

Exact low-temperature series coefficients obtained.

Phase transition explained through energy cluster model.

Method applicable to other lattice models.

Abstract

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic--to--paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.