Zero-Temperature Dynamics of ± J Spin Glasses and Related Models

We study zero-temperature, stochastic Ising models σ on Z with (disordered) 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, σ 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.