Population Annealing Simulations of a Binary Hard Sphere Mixture

TL;DR

This paper demonstrates that population annealing, a parallel Monte Carlo method, effectively simulates equilibrium states of a binary hard sphere mixture, providing precise equations of state and insights into jamming transitions.

Contribution

The study applies population annealing to a binary hard sphere mixture, showing its effectiveness in exploring glassy regimes and jamming phenomena.

Findings

Accurate equation of state up to packing fraction 0.60

Deviations from BMCSL equation observed at high densities

Jamming predicted at packing fraction approximately 0.667

Abstract

Population annealing is a sequential Monte Carlo scheme well-suited to simulating equilibrium states of systems with rough free energy landscapes. Here we use population annealing to study a binary mixture of hard spheres. Population annealing is a parallel version of simulated annealing with an extra resampling step that ensures that a population of replicas of the system represents the equilibrium ensemble at every packing fraction in an annealing schedule. The algorithm and its equilibration properties are described and results are presented for a glass-forming fluid composed of a 50/50 mixture of hard spheres with diameter ratio of 1.4:1. For this system, we obtain precise results for the equation of state in the glassy regime up to packing fractions $\varphi \approx 0.60$ and study deviations from the BMCSL equation of state. For higher packing fractions, the algorithm falls out of equilibrium and a free volume fit predicts jamming at packing fraction $\varphi \approx 0.667$. We conclude that population annealing is an effective tool for studying equilibrium glassy fluids and the jamming transition.