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A ``persistence'' exponent theta has been extensively used to describe thenonequilibrium dynamics of spin systems following a deep quench: forzero-temperature homogeneous Ising models on the d-dimensional cubic lattice,the fraction p(t) of spins not flipped by time t decays to zero liket^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, becauseof ``blocking'' (but perhaps still like a power). What are the effects ofdisorder or changes of lattice? We show that these can quite generally lead toblocking (and convergence to a metastable configuration) even for low d, andthen present two examples --- one disordered and one homogeneous --- where p(t)decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter

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