Bipartite dimer representation of squared 2d-Ising correlations

TL;DR

This paper provides a new, more direct proof of the Bozonisation identities linking squared 2D Ising correlations to bipartite dimer partition functions, enhancing understanding of order and disorder in XOR-Ising configurations.

Contribution

It introduces a novel, streamlined proof of existing identities, improving clarity and tracking of order and disorder in XOR-Ising models.

Findings

New proof of Bozonisation identities using a different approach

Enhanced understanding of order and disorder in XOR-Ising configurations

Clarification of the relationship between Ising correlations and dimer models

Abstract

The Bozonisation identities of [Dub11] show that squared 2d-Ising order and disorder correlations are equal to +- the ratio of bipartite dimer partition functions. In this self-contained paper, we give another proof of these identities using the approach of [BdT14]. Our proof is more direct and allows to keep track of order and disorder in XOR-Ising configurations.