Critical Nonequilibrium Cluster-flip Relaxations in Ising Models

TL;DR

This study explores how nonequilibrium cluster-flip relaxations in Ising models transition from stretched-exponential to power-law behavior as dimensionality increases, highlighting the role of finite-size scaling analysis.

Contribution

It reveals the dimensionality-dependent change in relaxation dynamics and demonstrates the effectiveness of finite-size scaling analysis using normalized correlation length.

Findings

Two- and three-dimensional models show stretched-exponential relaxation.

Four- and infinite-dimensional models exhibit power-law relaxation.

Finite-size scaling with normalized correlation length improves analysis accuracy.

Abstract

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched-exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.