Persistence of Manifolds in Nonequilibrium Critical Dynamics

TL;DR

This paper analytically and numerically investigates the decay behavior of manifold magnetization persistence in critical spin systems, revealing distinct decay forms depending on system parameters and providing specific predictions for 2D and 3D Ising models.

Contribution

It introduces a unified analytical framework for the persistence decay of manifolds in critical dynamics, classifying decay forms based on a key parameter and validating predictions with numerical simulations.

Findings

Power-law decay for line magnetization in 2D Ising model.

Power-law decay for plane magnetization in 3D Ising model.

Stretched exponential decay for line magnetization in 3D Ising model.

Abstract

We study the persistence P(t) of the magnetization of a d' dimensional manifold (i.e., the probability that the manifold magnetization does not flip up to time t, starting from a random initial condition) in a d-dimensional spin system at its critical point. We show analytically that there are three distinct late time decay forms for P(t) : exponential, stretched exponential and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d' and \eta, z are standard critical exponents. In particular, our theory predicts that the persistence of a line magnetization decays as a power law in the d=2 Ising model at its critical point. For the d=3 critical Ising model, the persistence of the plane magnetization decays as a power law, while that of a line magnetization decays as a stretched exponential. Numerical results are consistent with these analytical predictions.