A hard-sphere model on generalized Bethe lattices: Statics

TL;DR

This paper investigates a hard-sphere model on a generalized Bethe lattice with loops, revealing multiple phases including liquid, crystalline, glassy, and crystalline glassy states, supported by analytical and Monte Carlo methods.

Contribution

It introduces a detailed phase diagram analysis of a hard-sphere model on a generalized Bethe lattice with loops, highlighting new crystalline and glassy phases.

Findings

Identification of multiple phases including liquid, crystalline, glassy, and crystalline glassy.

Analytical phase diagram supported by Monte Carlo simulations.

Insights into the close-packing limit in the glassy phase.

Abstract

We analyze the phase diagram of a model of hard spheres of chemical radius one, which is defined over a generalized Bethe lattice containing short loops. We find a liquid, two different crystalline, a glassy and an unusual crystalline glassy phase. Special attention is also paid to the close-packing limit in the glassy phase. All analytical results are cross-checked by numerical Monte-Carlo simulations.