A General Limitation on Monte Carlo Algorithms of Metropolis Type

Details A General Limitation on Monte Carlo Algorithms of Metropolis Type A General Limitation on Monte Carlo Algorithms of Metropolis Type

1993-07-28

arxiv.org/abs/hep-lat/9307021v1

Phys.Rev.Lett.72:179-182,1994

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages, LaTeX plus subeqnarray.sty (included at end), NYU-TH-93/07/01, IFUP-TH33/93

Scientific paper

10.1103/PhysRevLett.72.179

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 $\pi$ and the probability distribution $\pi^{(0)}$ 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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