# Crystalline ordering and large fugacity expansion for hard core lattice particles

## TL;DR

This paper proves phase transitions and sublattice orderings in certain hard core lattice particle systems using an extension of Pirogov-Sinai theory, and demonstrates the convergence of the Gaunt-Fisher expansion for pressure.

## Contribution

It extends Pirogov-Sinai theory to a broad class of hard core lattice particles and establishes the convergence of the pressure expansion in inverse fugacity.

## Key findings

- Proves phase transitions for systems with finite close packed configurations.
- Shows the Gaunt-Fisher expansion has a nonzero radius of convergence.
- Includes many previously unproven cases of sublattice ordering.

## Abstract

Using an extension of Pirogov-Sinai theory we prove phase transitions, corresponding to sublattice orderings, for a general class of hard core lattice particle systems with a finite number of close packed configurations. These include many cases for which such transitions have been proven. The proof also shows that, for these systems, the Gaunt-Fisher expansion of the pressure in powers of the inverse fugacity (aside from an explicit logarithmic term) has a nonzero radius of convergence.