Abstract polymer models with general pair interactions

TL;DR

The paper introduces a convergence criterion for cluster expansions in abstract polymer systems with general pair interactions and applies it to analyze the low temperature phase of a long-range BEG model.

Contribution

It provides a new convergence criterion applicable to systems with non-hard-core, non-repulsive interactions and demonstrates its use on a long-range BEG model.

Findings

Established a convergence criterion for general pair interactions.

Analyzed the low temperature phase of a long-range BEG model.

Demonstrated applicability to models with polynomial decay interactions.

Abstract

A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of the BEG model with infinite range interactions, decaying polynomially as $1/r^{d+\lambda}$ with $\lambda>0$, is studied.