Polynomial algorithm for exact calculation of partition function for binary spin model on planar graphs

TL;DR

This paper presents a polynomial-time algorithm with O(N^2) complexity for exactly computing the partition function of binary spin models on planar graphs, validated against Onsager's solution for the 2D Ising model.

Contribution

It introduces a new efficient polynomial algorithm for exact partition function calculation on planar graphs with binary spins, with publicly available implementation.

Findings

Algorithm runs in O(N^2) time

Results agree with Onsager's analytical solution

Code is publicly accessible

Abstract

In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity of the algorithm is O(N^2). Test experiments shows good agreement with Onsager's analytical solution for two-dimensional Ising model of infinite size.