Nested sampling for materials: the case of hard spheres

TL;DR

This paper applies nested sampling to the three-dimensional hard sphere model, enabling direct calculation of thermodynamic properties and providing insights into phase transitions, crystallinity, and jammed states in condensed matter systems.

Contribution

It demonstrates the use of nested sampling for condensed phase systems, allowing direct computation of the partition function and related thermodynamic quantities.

Findings

Transition to crystallinity has a small free energy barrier.

Jammed states contribute negligibly to free energy above the phase transition.

Maximally random jammed configurations are surprisingly disordered.

Abstract

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.