Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

C. M. Newman; D. L. Stein

doi:10.1103/physrevlett.82.3944

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Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

C. M. Newman·D. L. Stein

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Abstract

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).

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C. M. Newman, D. L. Stein. 1999-04-14. Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models. https://doi.org/10.1103/physrevlett.82.3944

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