Fluid-solid transition in hard hyper-sphere systems

TL;DR

This study uses molecular dynamics simulations to estimate the freezing points of hard hypersphere systems in dimensions 4 to 7, revealing a nearly continuous change in RDF indicative of a second order phase transition.

Contribution

It introduces a numerical method to estimate the freezing point across dimensions using RDF analysis and semiempirical fits, extending known results to higher dimensions.

Findings

RDF minimum height change suggests second order transition

Estimated freezing points align with previous data up to D=6

New freezing point estimates provided for D=7

Abstract

In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the Radial Distribution Function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3) it was observed that the height of the first minimum of the RDF changes in an almost continuous way around the freezing density and resembles a second order phase transition. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the estimated values of the freezing point are very close to previously reported values from simulations and theoretical approaches up to D = 6 reinforcing the validity of the proposed method. This was also applied to numerical simulations for D = 7 giving new estimations of the freezing point for this dimensionality.