A first-order phase-transition, a super-cooled fluid, and a glass in a two-dimensional lattice gas model

TL;DR

This paper investigates a two-dimensional lattice gas model revealing a first-order phase transition, a super-cooled fluid, and a glassy state, providing insights into the thermodynamics of glass formation.

Contribution

It demonstrates the existence of a thermodynamic metastable glassy phase with finite Edwards' compactivity through series expansion analysis.

Findings

Evidence for a first-order phase transition with finite density and entropy jump.

Identification of a super-cooled fluid branch extending beyond the critical point.

The termination density of the super-cooled fluid aligns with the random-closest-packing density of the glass.

Abstract

Studying the series expansion of the thermodynamic potential for the hard-core N3 lattice-gas model, we provide evidence for a first-order phase-transition with a finite jump in density and entropy, in agreement with numerical transfer matrix calculations. The solid branch terminates at the transition, while the fluid branch continues beyond the critical activity, describing a meta-stable super-cooled fluid. It terminates with density 0.85 (relative to the closest packing density) and finite entropy per site. This termination density is close to the random-closest-packing density of the glassy state obtained for infinitely-fast cooling. The model thus exhibits a thermodynamic meta-stable glassy phase with finite Edwards' compactivity.