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1D Aging

L. R. Fontes·M. Isopi·C. M. Newman·D. L. Stein
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Abstract

We derive exact expressions for a number of aging functions that are scaling limits of non-equilibrium correlations, R(tw,tw+t) as tw --> infinity with t/tw --> theta, in the 1D homogenous q-state Potts model for all q with T=0 dynamics following a quench from infinite temperature. One such quantity is (the two-point, two-time correlation function) when n/sqrt(tw) --> z. Exact, closed-form expressions are also obtained when one or more interludes of infinite temperature dynamics occur. Our derivations express the scaling limit via coalescing Brownian paths and a ``Brownian space-time spanning tree,'' which also yields other aging functions, such as the persistence probability of no spin flip at 0 between tw and tw+t.

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L. R. Fontes, M. Isopi, C. M. Newman, D. L. Stein. 2001-03-23. 1D Aging. https://doi.org/10.1103/physrevlett.87.110201

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