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 $n$-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 $n$-fold way algorithms.

• Received 3 June 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.1