Vol. 3, No. 1, 2008

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Monte Carlo without chains

Alexandre J. Chorin

Vol. 3 (2008), No. 1, 77–93
Abstract

A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the Edwards–Anderson spin glass in three dimensions.

Keywords
Monte Carlo, no Markov chain, marginal, spin glass
Mathematical Subject Classification 2000
Primary: 82D30, 65C20
Milestones
Received: 5 February 2008
Revised: 9 July 2008
Accepted: 9 July 2008
Published: 19 July 2008
Authors
Alexandre J. Chorin
Department of Mathematics
Evans Hall, University of California
Berkeley, CA 94720
United States