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Persistence in One-dimensional Ising Models with Parallel Dynamics

G. I. Menon·P. Ray·P. Shukla
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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.

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G. I. Menon, P. Ray, P. Shukla. 2001-07-03. Persistence in One-dimensional Ising Models with Parallel Dynamics. https://doi.org/10.1103/physreve.64.046102

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