Monte Carlo Simulation of Universal Short-Time Behavior in Critical Relaxation

TL;DR

This paper uses Monte Carlo simulations to study the short-time dynamics of the 3D critical Ising model, confirming theoretical predictions about initial magnetization growth and decay behavior.

Contribution

It provides numerical verification of the universal short-time behavior and initial exponent in the critical relaxation of the 3D Ising model.

Findings

Confirmed the initial increase of magnetization as predicted.

Determined the initial exponent theta' with high accuracy.

Analyzed the long-time decay dependence on initial conditions.

Abstract

The time evolution of the three-dimensional critical Ising model relaxing from a nonequilibrium initial state is studied by means of Monte Carlo simulation. We observe the characteristic initial increase of the (spatially) averaged magnetization predicted by Janssen et al. The exponent theta' that governs the initial behavior is determined, and the dependence of the long-time linear decay on the initial magnetization analyzed. Our simulation corroborates earlier results derived from continuum models.