Short-time dynamics and critical behavior of three-dimensional site-diluted Ising model

TL;DR

This study uses Monte Carlo simulations to explore the short-time dynamic behavior and critical exponents of a three-dimensional weakly site-diluted Ising model, revealing a crossover from pure to disordered critical behavior.

Contribution

It provides new insights into the crossover phenomenon and determines static and dynamic critical exponents considering corrections to scaling for the diluted Ising model.

Findings

Identification of three stages of dynamic evolution

Determination of universal critical exponents

Comparison with previous numerical and theoretical results

Abstract

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations $p=0.95$ and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.