  We investigate the final state of zero-temperature Ising ferromagnets which
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 either reaches a frozen stripe state with probability
approximately equal to 1/3 or the ground state with probability approximately
equal to 2/3. In greater than two dimensions, the probability to reach the
ground state or a frozen state rapidly vanishes as the system size increases
and the system wanders forever in an iso-energy 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
non-zero temperature, relaxation to the final state first proceeds by the
formation of very long-lived metastable states, similar to the zero-temperature
case, before equilibrium is reached.
