Fate of zero-temperature Ising ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 3/10 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales with the longer stemming from the influence of a long-lived diagonal stripe defect. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically “blinking” metastable states.