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Center for Nonlinear Studies |
What is the fate of a finite-size homogeneous Ising model that is prepared at infinite temperature and subsequently evolves by zero-temperature Glauber dynamics? In one dimension, the ground state is always reached. In two dimensions, the ground state is reached in only about 2/3 of all realizations, and the long-time evolution is characterized by two distinct time scales. We also relate the probability of reaching the ground state in terms of exactly-calculated percolation crossing probabilities. In three dimensions, the evolution is much richer still. Specifically: (i) Domains at long time are strongly interpenetrating and topologically complex, with their average genus growing algebraically with system size; (ii) The long-time state almost always contains "blinker" spins that can flip ad infinitum with no energy cost. (iii) The relaxation is characterized by multiple time scales, the longest of which grows exponentially with system size.
Host: Sasha Gutfraind, T-5, CNLS, gutfraind@lanl.gov