Blocking and persistence in the zero-temperature dynamics of homogeneous and disordered Ising models

A "persistence" exponent theta has been extensively used to describe the no nequilibrium dynamics of spin systems following a deep quench: For zero-tem perature homogeneous Ising models on the d-dimensional cubic lattice Z(d), the fraction p(t) of spins not flipped by time t decays to zero like t(-the ta(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 disor der or changes of the 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).