Phase transitions in systems of particles with only hard-core interactions

TL;DR

This paper reviews the current understanding of phase transitions in hard-core particle systems, discussing equations of state, singularities, and mesophases, highlighting recent theoretical insights and models.

Contribution

It provides a comprehensive overview of phase transition phenomena in hard-core systems, connecting various models and recent developments in the field.

Findings

Analysis of the hard sphere gas equation of state in multiple dimensions

Discussion of Lee-Yang singularities and their relation to polymer models

Insights into orientationally disordered crystalline mesophases

Abstract

This article contains our comments and views on the status of the current understanding of phase transitions in systems with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in $d$-dimensions is discussed. The universal repulsive Lee-Yang singularities in the complex activity plane, and its relation to the directed and undirected polymer models are outlined. We also discuss orientationally disordered crystalline mesophases, and some of their models.