Fate of Zero-Temperature Ising Ferromagnets
V. Spirin, P. L. Krapivsky, S. Redner
Abstract
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 1/4 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.
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