High-fugacity expansion, Lee-Yang zeros and order-disorder transitions in hard-core lattice systems

TL;DR

This paper proves the existence of order-disorder phase transitions in certain hard-core lattice systems and shows that their pressure and correlations can be expanded in powers of inverse fugacity, indicating Lee-Yang zeros lie in a finite annulus.

Contribution

It establishes phase transitions and convergent expansions for a class of non-sliding hard-core lattice systems, linking Lee-Yang zeros to system properties.

Findings

Order-disorder phase transitions are proven for non-sliding hard-core lattice systems.

Pressure and correlation functions have convergent expansions in inverse fugacity.

Lee-Yang zeros are confined to an annulus with finite positive radii.

Abstract

We establish existence of order-disorder phase transitions for a class of "non-sliding" hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a finite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee-Yang zeros lie in an annulus with finite positive radii.