Non-Markovian Persistence and Nonequilibrium Critical Dynamics

TL;DR

This paper calculates the persistence exponent for critical dynamics in non-Markovian systems, revealing it as a new exponent and employing a perturbation theory approach around Markov processes.

Contribution

It introduces a perturbation theory to compute the persistence exponent in non-Markovian critical dynamics, showing that this exponent is fundamentally new.

Findings

Calculated  to second order for model A

Demonstrated  as a new exponent at this order

Showed that the process is non-Markovian at this order

Abstract

The persistence exponent \theta for the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time interval t following the quench. We calculate \theta to O(\epsilon^2) for model A of critical dynamics (and to order \epsilon for model C) and show that at this order M(t) is a non-Markov process. Consequently, \theta is a new exponent. The calculation is performed by expanding around a Markov process, using a simplified version of the perturbation theory recently introduced by Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].