A hard-sphere model on generalised Bethe lattices: Dynamics

TL;DR

This paper investigates the dynamics of a hard-sphere lattice gas on generalized Bethe lattices using a projective approximation scheme, analyzing phase transitions, equilibration times, and validating results with simulations.

Contribution

It introduces a projective approximation scheme to analyze non-equilibrium dynamics on generalized Bethe lattices, focusing on phase transitions and equilibration.

Findings

Predicted divergence of equilibration times near phase transitions.

Validated analytical results with Monte-Carlo simulations.

Analyzed liquid-crystal and liquid-spin-glass transitions.

Abstract

We analyse the dynamics of a hard-sphere lattice gas on generalised Bethe lattices using a projective approximation scheme (PAS). The latter consists in mapping the system's dynamics to a finite set of global observables, closure of the resulting equations is obtained by approximating the true non-equilibrium state by a pseudo-equilibrium based only on the value of the observables under consideration. We study the liquid--crystal as well as the liquid--spin-glass transitions, special attention is given to the prediction of equilibration times and their divergence close to the phase transitions. Analytical results are corroborated by Monte-Carlo simulations.