Aging in 1D Discrete Spin Models and Equivalent Systems

We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(t(w),t(w)+t) as t(w)-->infinity, t/t(w)-->theta, in the 1D homogenous q-state Potts model for all q with T = 0 dynamics following a quench from T = infinity. One such quantity...

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Bibliographic Details
Published in:Physical review letters 2001-09, Vol.87 (11), p.110201-110201, Article 110201
Main Authors: Fontes, L R, Isopi, M, Newman, C M, Stein, D L
Format: Article
Language:English
Subjects:
AGING
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
PROBABILITY
SPACE-TIME
SPIN
SPIN FLIP
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Summary:We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(t(w),t(w)+t) as t(w)-->infinity, t/t(w)-->theta, in the 1D homogenous q-state Potts model for all q with T = 0 dynamics following a quench from T = infinity. One such quantity is (0)(t(w));sigma-->(n)(t(w)+t)> when n/square root of ([t(w))-->z. Exact, closed-form expressions are also obtained when an interlude of T = infinity dynamics occurs. 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 t(w) and t(w)+t.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.87.110201