Universality and Scaling in Short-time Critical Dynamics

TL;DR

This paper investigates the short-time critical dynamics of 2D Ising and Potts models, confirming universality and scaling through numerical simulations and analysis of critical exponents.

Contribution

It introduces new measurements of the dynamic critical exponent θ and confirms universality across different algorithms and models.

Findings

Critical initial increase of magnetization observed

Consistent determination of exponents θ, z, and 2β/ν

Universality and scaling confirmed across methods

Abstract

Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the magnetization is observed. The new dynamic critical exponent $\theta$ as well as the exponents $z$ and $2\beta/\nu$ are determined from the power law behaviour of the magnetization, auto-correlation and the second moment. Furthermore the calculation has been carried out with both Heat-bath and Metropolis algorithms. All the results are consistent and therefore universality and scaling are confirmed.