English

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

Disordered Systems and Neural Networks 2009-10-31 v1 Statistical Mechanics Probability

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).

Keywords

Cite

@article{arxiv.cond-mat/9904208,
  title  = {Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models},
  author = {C. M. Newman and D. L. Stein},
  journal= {arXiv preprint arXiv:cond-mat/9904208},
  year   = {2009}
}

Comments

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