Freezing in Ising ferromagnets

Abstract

We investigate the final state of zero-temperature Ising ferromagnets that are endowed with single-spin-flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the system reaches either a frozen stripe state with probability approximately 1/3 or the ground state with probability approximately 2/3. In greater than two dimensions, the probability of reaching the ground state or a frozen state rapidly vanishes as the system size increases; instead the system wanders forever in an isoenergy set of metastable states. An external magnetic field changes the situation drastically-in two dimensions the favorable ground state is always reached, while in three dimensions the field must exceed a threshold value to reach the ground state. For small but nonzero temperature, relaxation to the final state proceeds first by formation of very long-lived metastable states, as in the zero-temperature case, before equilibrium is reached.