A general limitation on Monte Carlo algorithms of the Metropolis type

We prove that for any Monte Carlo algorithm of Metropolis type, the autocorraletion 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 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 nonlocal algorithms.