A Generalization of Metropolis and Heat-Bath Sampling for Monte Carlo Simulations

TL;DR

This paper introduces a generalized Monte Carlo sampling method that guarantees convergence to a target distribution, allowing for unconditional acceptance of moves and potentially improving efficiency over traditional Metropolis algorithms.

Contribution

It proposes a new sampling approach based on local phase space regions and square root probabilities, extending Metropolis and Heat-Bath methods with theoretical validation.

Findings

Method guarantees convergence to the desired distribution

Allows for unconditional acceptance of trial moves

Demonstrated utility through numerical experiments

Abstract

For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that it is sometimes possible to arrange for unconditional acceptance of trial moves. It involves sampling states in a local region of phase space with probability equal to, in the first approximation, the square root of the desired global probability density function. The validity of this choice is derived from the Chapman-Kolmogorov equation, and the utility of the method is illustrated by a prototypical numerical experiment.