New convergence bound for the cluster expansion in canonical ensemble

TL;DR

This paper introduces a novel polymer activity choice in the canonical ensemble's cluster expansion, resulting in an improved convergence bound and applicability to various boundary conditions and correlation expansions.

Contribution

It presents a new convergence bound for the cluster expansion in the canonical ensemble using a different polymer activity choice, enhancing previous results.

Findings

Improved convergence bound for the cluster expansion.

Applicability to zero boundary conditions and correlation expansions.

Recovery of irreducible Mayer coefficients for free energy.

Abstract

We perform a cluster expansion in the canonical ensemble with periodic boundary conditions, introducing a new choice of polymer activities that differs from the standard ones. This choice leads to an improved bound for the convergence of the cluster expansion, which we compare with the known one. We also recover the irreducible Mayer coefficients for the thermodynamic free energy. The results presented here can also be applied to the case of zero boundary conditions and to the convergence of correlation expansions.