Exact bosonization of the Ising model

TL;DR

This paper introduces exact combinatorial bosonization identities linking Ising model correlators with free field correlators, utilizing the height function of bipartite dimer models, with applications to asymptotic analysis.

Contribution

It provides the first exact combinatorial bosonization identities for the Ising model, connecting correlators with free fields via height functions.

Findings

Established exact combinatorial identities for Ising correlators.

Linked Ising correlators to bipartite dimer height functions.

Discussed applications to asymptotic behavior of correlators.

Abstract

We present exact combinatorial versions of bosonization identities, which equate the product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete free field is played by the height function of an associated bipartite dimer model. Some applications to the asymptotic analysis of Ising correlators are discussed.