Critical Phenomena in Quasi-Two-Dimensional Vibrated Granular Systems

TL;DR

This study uses molecular dynamics simulations to analyze critical phenomena in quasi-two-dimensional vibrated granular systems, revealing a complex phase transition behavior with tricritical points and critical exponents consistent with experiments.

Contribution

It identifies the phase diagram and critical properties of the liquid-solid transition, including the existence of a tricritical point and the critical exponent $eta=1/2$, through simulation.

Findings

Transition line merges at a tricritical point.

Critical exponent $eta=1/2$ matches experimental results.

Fluctuations of $ ext{chi}_4$ do not show critical behavior.

Abstract

The critical phenomena associated to the liquid to solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are associated to the fourfold bond-orientational order parameter $\chi_4$, which measures the level of square crystallization of the system. Previous experimental results have shown that the transition of $\chi_4$, when varying the vibration amplitude, can be either discontinuous or continuous, for two different values of the height of the box. Exploring the amplitude-height phase space, a transition line is found, which can be either discontinuous or continuous, merging at a tricritical point and the continuous branch ends in an upper critical point. In the continuous transition branch, the critical properties are studied. The exponent associated to the amplitude of the order parameter is $\beta=1/2$, for various system sizes, in complete agreement with the experimental results. However, the fluctuations of $\chi_4$ do not show any critical behavior, probably due to crossover effects by the close presence of the tricritical point. Finally, in quasi-one-dimensional systems, the transition is only discontinuous, limited by one critical point, indicating that two is the lower dimension for having a tricritical point.