Persistence in one-dimensional Ising models with parallel dynamics.

Abstract

We study persistence in one-dimensional ferromagnetic and antiferromagnetic 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) approximately 1/t(straight theta(p)) with straight theta(p) approximately 0.75 numerically. A mapping to the dynamics of two decoupled A+A-->0 models yields straight 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.