Zero-temperature dynamics of ± J spin glasses and related models

We study zero-temperature, stochastic Ising models sigma (1) on Z(d) with (disordered) nearest-neighbor couplings independently chosen from a distribution mu on R and an initial spin configuration chosen uniformly at random. Given d, call mu type I (resp., type F) if, for every x in Z(d), sigma (t)(x) flips infinitely (resp.. only finitely) many times as t --> infinity (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 mu is easy to determine, The main result of this: paper is a proof that for d = 2, +/- J models (where mu = alpha delta (J) + (1 - alpha)delta - (J)) are type M, unlike homogeneous models: (type Zi or continuous (finite mean) mu 's (type F). We also prove that all other noncontinuous disordered systems an type M fur any d greater than or equal to 2. The +/-J proof is noteworthy in that it is much less "local" than the other (simpler) proof, Homogeneous and +/-J models for d greater than or equal to 3 remain an open problem.