1D Aging
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) <sigma(0,tw) sigma(n,tw+t)> 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.
Keywords
Cite
@article{arxiv.cond-mat/0103494,
title = {1D Aging},
author = {L. R. Fontes and M. Isopi and C. M. Newman and D. L. Stein},
journal= {arXiv preprint arXiv:cond-mat/0103494},
year = {2009}
}
Comments
4 pages (RevTeX); 2 figures; submitted to Physical Review Letters