Abstract
In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.
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Baker, G.A. A Markov-property Monte Carlo method: One-dimensional Ising model. J Stat Phys 72, 621–641 (1993). https://doi.org/10.1007/BF01048026
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DOI: https://doi.org/10.1007/BF01048026