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A class of Monte Carlo algorithms which incorporate absorbing Markov chainsis presented. In a particular limit, the lowest-order of these algorithmsreduces to the $n$-fold way algorithm. These algorithms are applied to studythe escape from the metastable state in the two-dimensional square-latticenearest-neighbor Ising ferromagnet in an unfavorable applied field, and theagreement with theoretical predictions is very good. It is demonstrated thatthe higher-order algorithms can be many orders of magnitude faster than eitherthe traditional Monte Carlo or $n$-fold way algorithms.Comment: ReVTeX, Request 3 figures from novotny@scri.fsu.ed

Monte Carlo Algorithms with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics