Finite Size Scaling and Critical Exponents in Critical Relaxation

TL;DR

This paper introduces a new finite size scaling method to measure dynamic and static critical exponents during the early-time critical relaxation of the 2D Ising model, providing accurate estimates from time-dependent data.

Contribution

The authors develop a novel approach using finite size scaling at early times to simultaneously determine dynamic and static critical exponents in the 2D Ising model.

Findings

Successfully measured the dynamical exponent z from the Binder cumulant.

Determined static exponents β/ν and ν from magnetization evolution.

Validated the method's effectiveness for critical relaxation analysis.

Abstract

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent $z$ is extracted independently, while the static exponents $\beta/\nu$ and $\nu$ are obtained from the time evolution of the magnetization and its higher moments.