Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model

Abstract

We study the decay of the probability for a non-Markovian stationary Gaussian walker not to cross the origin up to time $t$. This result is then used to evaluate the fraction of spins that do not flip up to time $t$ in the zero temperature Monte-Carlo spin flip dynamics of the Ising model. Our results are compared to extensive numerical simulations.

13 pages RevTeX. Updated and corrected version accepted for publication (11th July 96) in Physical Review Letters

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