Exact Solution for Partition function of General Ising Model in Magnetic Fields and Bayesian Networks

TL;DR

This paper introduces an exact method for computing the partition function of the Ising model in magnetic fields for arbitrary shapes, linking it to Bayesian networks and enabling applications in data science.

Contribution

It presents a novel matrix-based approach to exactly solve the Ising model in magnetic fields for complex structures and connects this to Bayesian network solutions.

Findings

Exact partition function calculation for arbitrary shapes

Method applicable to infinite-scale crystal systems

Connection established between Ising models and Bayesian networks

Abstract

We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices that are created automatically based on the structure of the system. By generalizing this method, it becomes possible to calculate the partition function of various crystal systems (network shapes) in magnetic fields when N (scale) is infinite. Furthermore, we also connect this method for finding the solution to the Ising model in magnetic fields to a method for finding the solution to Bayesian networks in information statistical mechanics (applied to data mining, machine learning, and combinatorial optimization).