Relaxational dynamics in 3D randomly diluted Ising models

TL;DR

This study investigates the relaxational critical dynamics of three-dimensional disordered Ising models, confirming a universal dynamic critical exponent and demonstrating consistent equilibrium and off-equilibrium behaviors through Monte Carlo simulations.

Contribution

It provides the first comprehensive Monte Carlo analysis confirming a universal dynamic universality class for disordered 3D Ising models and estimates the dynamic critical exponent z=2.35(2).

Findings

Universal dynamic critical exponent z=2.35(2)

Consistent equilibrium and off-equilibrium dynamics

Confirmation of a single dynamic universality class

Abstract

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).