Marked Gibbs measures via cluster expansion

TL;DR

This paper constructs marked Gibbs measures using cluster expansion in high temperature and low fugacity regimes, applicable to various models in classical and quantum statistical physics.

Contribution

It provides a detailed construction of marked Gibbs measures for a broad class of spaces and potentials, extending to standard Borel spaces.

Findings

Successful construction of marked Gibbs measures via cluster expansion

Applicable to classical and quantum statistical physics models

Extension to more general spaces like standard Borel spaces

Abstract

We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability conditions are satisfied. That is, for state space we take a locally compact separable metric space $X$ and a separable metric space $S$ for the mark space. This framework allowed us to cover several models of classical and quantum statistical physics. Furthermore, we also show how to extend the construction for more general spaces as e.g., separable standard Borel spaces. The construction of the marked Gibbs measures is based on the method of cluster expansion.