1D Aging

Details 1D Aging 1D Aging

2001-03-23

arxiv.org/abs/cond-mat/0103494v1

Phys. Rev. Lett. 87, (2001), 110201-1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages (RevTeX); 2 figures; submitted to Physical Review Letters

Scientific paper

10.1103/PhysRevLett.87.110201

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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