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

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

1999-04-14

arxiv.org/abs/cond-mat/9904208v1

Phys. Rev. Lett., 82 (1999) 3944

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages (LaTeX); to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.82.3944

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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