Monte Carlo algorithms with absorbing Markov chains: Fast local algorithms for slow dynamics.

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest order of these algorithms reduces to the [ital n]-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or [ital n]-fold way algorithms.