Freezing in Ising ferromagnets

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 $\approx 1/3$ or the ground state with probability $\approx 2/3.$ 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.