Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models

Details Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models

2000-05-10

arxiv.org/abs/cond-mat/0005180v1

Phys. Rev. E 62, 3366 (2000)

Physics

Condensed Matter

Statistical Mechanics

RevTex, 11 pages

Scientific paper

10.1103/PhysRevE.62.3366

The distribution, n(k,t), of the interval sizes, k, between clusters of persistent sites in the dynamical evolution of the one-dimensional q-state Potts model is studied using a combination of numerical simulations, scaling arguments, and exact analysis. It is shown to have the scaling form n(k,t) = t^{-2z} f(k/t^z), with z= max(1/2,theta), where theta(q) is the persistence exponent which characterizes the fraction of sites which have not changed their state up to time t. When theta > 1/2, the scaling length, t^theta, for the interval-size distribution is larger than the coarsening length scale, t^{1/2}, that characterizes spatial correlations of the Potts variables.

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