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arXiv · hep-lat/9307021

A General Limitation on Monte Carlo Algorithms of Metropolis Type

Sergio Caracciolo·Andrea Pelissetto·Alan D. Sokal
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Abstract

We prove that for any Monte Carlo algorithm of Metropolis type, the autocorrelation time of a suitable ``energy''-like observable is bounded below by a multiple of the corresponding ``specific heat''. This bound does not depend on whether the proposed moves are local or non-local; it depends only on the distance between the desired probability distribution $π$ and the probability distribution $π^{(0)}$ for which the proposal matrix satisfies detailed balance. We show, with several examples, that this result is particularly powerful when applied to non-local algorithms.

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Sergio Caracciolo, Andrea Pelissetto, Alan D. Sokal. 1993-07-28. A General Limitation on Monte Carlo Algorithms of Metropolis Type. https://doi.org/10.1103/physrevlett.72.179

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