Fluid-solid transition in hard hyper-sphere systems

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.

13 pages, 10 figures

References in corpus (4)

• Packing Hyperspheres in High-Dimensional Euclidean Spaces
• Hard sphere crystallization gets rarer with increasing dimension
• Geometrical Frustration: A Study of 4d Hard Spheres
• Structure of hard-hypersphere fluids in odd dimensions

Cited by in corpus (8)

• Random Close Packing and the Hard Sphere Percus-Yevick Theory
• Structure characterization of hard sphere packings in amorphous and crystalline states
• Thermodynamic stability of hard sphere crystals in dimensions 3 through 10
• Three simple scenarios for high-dimensional sphere packings
• Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures
• Efficient $d$-dimensional molecular dynamics simulations for studies of the glass-jamming transition
• Structural transitions in hypersphere fluids: predictions of Kirkwood's approximation
• Equation of state for five-dimensional hyperspheres from the chemical-potential route