Persistence in One-dimensional Ising Models with Parallel Dynamics

Details Persistence in One-dimensional Ising Models with Parallel Dynamics Persistence in One-dimensional Ising Models with Parallel Dynamics

2001-07-03

arxiv.org/abs/cond-mat/0107053v1

Physics

Condensed Matter

Statistical Mechanics

5 pages Latex file, 3 postscript figures, to appear in Phys Rev. E

Scientific paper

10.1103/PhysRevE.64.046102

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.

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