Affinities and disagreements between Mean-field and short-range critical dynamics

TL;DR

This paper compares the critical dynamics of long-range mean-field systems with short-range systems through simulations, analyzing initial behaviors, critical points, and exponents in Ising and Blume-Capel models.

Contribution

It provides a detailed comparison of mean-field and short-range critical dynamics, including new simulation-based estimates of critical temperatures and exponents.

Findings

Mean-field and short-range dynamics show both similarities and differences in critical behavior.

Initial anomalous magnetization behavior is characterized and compared.

Critical exponents are independently calculated and agree with analytical results.

Abstract

In this work, we explore some interesting details of the time-dependent regime of the long-range systems under mean-field approximation in comparison with the critical dynamics of the short-range systems. First, we discuss some mechanisms of the initial anomalous behavior of the magnetization via two-dimensional Monte Carlo simulations to later compare with results from Mean-field simulations in both: spin 1/2 (Ising) and spin 1 (Blume Capel model) Ising models. The distinction between critical and tricritical points is also investigated. For a complete analysis, we performed short-time simulations in the mean-field regime to determine the critical temperatures optimizing power laws and the critical exponents of the different points, which were independently calculated, i.e. without using previous critical exponents estimates from literature/theory. Our investigations corroborate analytical results here also developed.