Integration Approach to Ising Models

TL;DR

This paper introduces an integral representation for the partition function of general n-dimensional Ising models, enabling analysis of their properties and providing an exact solution in a specific case.

Contribution

It presents a novel integral representation for Ising model partition functions, facilitating new analytical insights and an exact solution for a particular case.

Findings

Derived properties of the partition function using the integral representation

Provided an exact solution for a specific Ising model case

Extended the analysis to models with non-nearest neighbor interactions

Abstract

An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An exact solution is given in a particular case.