Partition functions of two-dimensional Ising models -- A perspective from Gauss hypergeometric functions

TL;DR

This paper expresses the partition functions and magnetization of 2D Ising models using Gauss hypergeometric functions, highlighting the role of critical exponents and the connection between approximations and exact solutions.

Contribution

It introduces a novel formulation of 2D Ising model partition functions via hypergeometric functions, linking heuristic susceptibility equations with critical exponents.

Findings

Partition functions expressed in terms of Gauss hypergeometric functions

Identification of the isomorphism between Bragg-Williams approximation and Onsager's solution

Clarification of how critical exponents influence partition functions

Abstract

Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss hypergeometric functions. The isomorphism existing between the Bragg-Williams approximation and the exact solution of Onsager is pointed out. The precise manner in which the critical exponents influence the partition functions is pointed out.