2001/03/23 by Luiz Renato Fontes, L. R. Fontes, Marco Isopi +4 · 1 citation
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.87.110201
published as Phys. Rev. Lett. 87, (2001), 110201-1 · 4 pages (RevTeX); 2 figures; submitted to Physical Review Letters
arxiv created 2001/03/23 · openalex publication_date 2001/08/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(tw,tw+t) as tw\ensuremath→\ensuremath∞, t/tw\ensuremath→\ensuremathθ, in the 1D homogenous q-state Potts model for all q with T\phantom\rule0ex0ex=\phantom\rule0ex0ex0 dynamics following a quench from T\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremath∞. One such quantity is 〈\stackrel\ensuremath→\ensuremathσ0(tw)\ifmmode \else \.\fi\stackrel\ensuremath→\ensuremathσn(tw+t)〉 when n/√tw\ensuremath→z. Exact, closed-form expressions are also obtained when an interlude of T\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremath∞ 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 tw and tw+t.