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

A ``persistence'' exponent θ 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 Zᵈ, the fraction $p(t)$ of spins not flipped by time t decays to zero like t^-θ(d) for low d; for high d, $p(t)$ may decay to p(∞)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder 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(∞).