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arXiv:cond-mat/0302537 · Physical Review Letters

Persistence of Manifolds in Nonequilibrium Critical Dynamics

Satya N. Majumdar, Alan J. Bray

Published Jul 18, 2003• 27 citations
arXivHTMLPDF

Abstract

We study the persistence probability $P(t)$ that, starting from a random initial condition, the magnetization of a ${d}^{\ensuremath{'}}$-dimensional manifold of a $d$-dimensional spin system at its critical point does not change sign up to time $t$. For ${d}^{\ensuremath{'}}>0$ we find three distinct late-time decay forms for $P(t)$: exponential, stretched exponential, and power law, depending on a single parameter $\ensuremath{\zeta}=(D\ensuremath{-}2+\ensuremath{\eta})/z$, where $D=d\ensuremath{-}{d}^{\ensuremath{'}}$ and $\ensuremath{\eta},z$ are standard critical exponents. In particular, we predict that for a line magnetization in the critical $d=2$ Ising model, $P(t)$ decays as a power law while, for $d=3$, $P(t)$ decays as a power of $t$ for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.

DOI
10.1103/physrevlett.91.030602

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