## Abstract

We study zero-temperature, stochastic Ising models σ^{t} on Z^{d} with (disor-dered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type I (resp., type F) if, for every x in Z^{d}, σ^{1}_{x} flips infinitely (resp., only finitely) many times as t → ∞ (with probability one) - or else mixed type M. Models of type I and M exhibit a zero-temperature version of "local non-equilibration". For d = 1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d = 2, ±J models (where μ = αδj + (1 - α)δ-j) are type M, unlike homogeneous models (type I) or continuous (finite mean) μ's (type F). We also prove that all other noncontinuous disordered systems are type M for any d ≥ 2. The ±J proof is noteworthy in that it is much less "local" than the other (simpler) proof. Homogeneous and ±J models for d ≥ 3 remain an open problem.

Original language | English (US) |
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Pages (from-to) | 373-387 |

Number of pages | 15 |

Journal | Communications In Mathematical Physics |

Volume | 214 |

Issue number | 2 |

DOIs | |

State | Published - Nov 2000 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics