2003/02/26 by Satya N. Majumdar, Alan J. Bray · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.91.030602
published as Phys. Rev. Lett. 91, 030602 (2003) · 4 pages revtex, 1 eps figure included
arxiv created 2003/02/26 · arxiv updated 2009/11/30
We study the persistence P(t) of the magnetization of a d' dimensional manifold (i.e., the probability that the manifold magnetization does not flip up to time t, starting from a random initial condition) in a d-dimensional spin system at its critical point. We show analytically that there are three distinct late time decay forms for P(t) : exponential, stretched exponential and power law, depending on a single parameter ζ=(D-2+η)/z where D=d-d' and η, z are standard critical exponents. In particular, our theory predicts that the persistence of a line magnetization decays as a power law in the d=2 Ising model at its critical point. For the d=3 critical Ising model, the persistence of the plane magnetization decays as a power law, while that of a line magnetization decays as a stretched exponential. Numerical results are consistent with these analytical predictions.