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Non-Markovian Persistence and Nonequilibrium Critical Dynamics

K. Oerding·S. J. Cornell·A. J. Bray
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Abstract

The persistence exponent θfor 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^{-θ}, that M(t) does not change sign in the time interval t following the quench. We calculate θto O(ε^2) for model A of critical dynamics (and to order εfor model C) and show that at this order M(t) is a non-Markov process. Consequently, θis 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].

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K. Oerding, S. J. Cornell, A. J. Bray. 1997-02-21. Non-Markovian Persistence and Nonequilibrium Critical Dynamics. https://doi.org/10.1103/physreve.56.r25

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