Persistence in One-dimensional Ising Models with Parallel Dynamics
Statistical Mechanics
2009-11-07 v1
Abstract
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p \simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0 models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.
Cite
@article{arxiv.cond-mat/0107053,
title = {Persistence in One-dimensional Ising Models with Parallel Dynamics},
author = {G. I. Menon and P. Ray and P. Shukla},
journal= {arXiv preprint arXiv:cond-mat/0107053},
year = {2009}
}
Comments
5 pages Latex file, 3 postscript figures, to appear in Phys Rev. E