A GENERAL LIMITATION ON MONTE-CARLO ALGORITHMS OF METROPOLIS TYPE

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 nonlocal; 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 nonlocal algorithms.