Low-temperature Metastability of Ising Models: Prefactors, Divergences, and Discontinuities

The metastable lifetime of the square-lattice and simple-cubic-lattice kinetic Ising models are studied in the low-temperature limit. The simulations are performed using Monte Carlo with Absorbing Markov Chain algorithms to simulate extremely long low-temperature lifetimes. The question being addressed is at what temperatures the mathematically rigorous low-temperature results become valid. It is shown that the answer depends partly on how close the system is to fields at which the prefactor for the metastable decay either has a discontinuity or diverges.