A note on Lee-Yang zeros in the negative half-plane

TL;DR

This paper investigates the relationship between Lee-Yang zeros and the thermodynamic properties of certain lattice systems, providing bounds on inverse compressibility and analyzing virial coefficients without a direct correlation.

Contribution

It establishes lower bounds on inverse compressibility for systems with Lee-Yang zeros in the left half-plane and explores the connection between virial coefficients and zero locations.

Findings

Lower bounds on inverse compressibility for systems with Lee-Yang zeros in the left half-plane.

No direct link between positivity of virial coefficients and negativity of Lee-Yang zeros.

Finite number of negative virial coefficients in the monomer-dimer system on two rows.

Abstract

We obtain lower bounds on the inverse compressibility of systems whose Lee-Yang zeros of the grand-canonical partition function lie in the left half of the complex fugacity plane. This includes in particular systems whose zeros lie on the negative real axis such as the monomer-dimer system on a lattice. We also study the virial expansion of the pressure in powers of the density for such systems. We find no direct connection between the positivity of the virial coefficients and the negativity of the L-Y zeros, and provide examples of either one or both properties holding. An explicit calculation of the partition function of the monomer-dimer system on 2 rows shows that there are at most a finite number of negative virial coefficients in this case.