Geometric expansion of the log-partition function of the anisotropic Heisenberg model

TL;DR

This paper derives the asymptotic expansion of the log-partition function for the anisotropic Heisenberg model in large domains, using cluster expansion and functional integrals.

Contribution

It provides explicit formulas for the non-decreasing terms of the expansion using a novel application of cluster expansion and trajectory representations.

Findings

Explicit asymptotic expansion terms derived

Functional integral representations obtained

Cluster expansion effectively applied to the model

Abstract

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.