Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

TL;DR

This study investigates the critical relaxation dynamics of the 2D Ising model using series expansion and Monte Carlo simulations, providing precise estimates of the dynamical critical exponent z.

Contribution

It combines series expansion and Monte Carlo methods to analyze the relaxation process and accurately estimate the dynamical critical exponent z.

Findings

Estimated z from series analysis is approximately 2.2.

Monte Carlo simulations yield z ≈ 2.169 with high precision.

Both methods are consistent within error margins.

Abstract

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.