Anomalous behavior of two-dimensional Hertzian sphere system

TL;DR

This study investigates the anomalous behaviors, including density and diffusion anomalies, in a two-dimensional Hertzian sphere system with molecular dynamics, revealing complex phase behavior and lattice oscillation effects.

Contribution

It is the first detailed analysis of anomalous behaviors and phase diagram features in a 2D Hertzian sphere system with exponent 7/2 using molecular dynamics.

Findings

Density anomaly observed in liquid, hexatic, and solid phases.

Density dependence of transverse phonon modes shows negative correlation.

Anomalous diffusion regions extend above the maximum melting temperature.

Abstract

The anomalous behavior of a two-dimensional system of Hertzian spheres with exponent $\alpha = 7/2 $ has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Water-like density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above maximum melting point $T = 0.0058$ of the triangular crystal. From analysis of the translational order parameter, which decreases with increasing density in the reentrant melting regions, the presence of a structural anomaly in the system has been assumed.