Stochastic Potential Switching Algorithm for Monte Carlo Simulations of Complex Systems

TL;DR

This paper introduces a stochastic potential switching Monte Carlo algorithm that maintains detailed balance while simplifying complex potentials, leading to significantly improved sampling efficiency in simulations of complex systems.

Contribution

A novel stochastic potential switching algorithm that enhances Monte Carlo simulations by reducing complexity and increasing efficiency while preserving detailed balance.

Findings

Achieved over tenfold increase in sampling efficiency.

Demonstrated effectiveness on a large Lennard-Jones fluid.

Reduced dynamic scaling exponent compared to Metropolis.

Abstract

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential $\tilde V$. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential $V$. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude.