Global Persistence Exponent for Critical Dynamics

TL;DR

This paper introduces and calculates the global persistence exponent $ heta$ for critical phenomena, demonstrating its independence as a new critical exponent through theoretical and numerical methods across various models.

Contribution

It defines the persistence exponent $ heta$ for nonequilibrium critical dynamics and computes it in multiple models, establishing it as a new independent critical exponent.

Findings

$ heta$ describes the probability decay of no sign change in the order parameter.

Calculated $ heta$ in mean-field, $O(n)$ limit, and 1D Ising model.

Numerical estimation of $ heta$ for 2D Ising model.

Abstract

A `persistence exponent' $\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \sim t^{-\theta}$, that the global order parameter has not changed sign in the time interval $t$ following a quench to the critical point from a disordered state. This exponent is calculated in mean-field theory, in the $n=\infty$ limit of the $O(n)$ model, to first order in $\epsilon = 4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $\theta$ is a new independent exponent.