title: Aging in 1D discrete spin models and equivalent systems.
abstract: 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 <sigma-->(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.
authors.affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, 05315-970 São Paulo, Brasil.
authors.forename: L R
authors.initials: LR
authors.lastname: Fontes
authors.forename: M
authors.initials: M
authors.lastname: Isopi
authors.forename: C M
authors.initials: CM
authors.lastname: Newman
authors.forename: D L
authors.initials: DL
authors.lastname: Stein