The convergence properties and stochastic characteristics inherent in force-biased and in metropolis Monte Carlo simulations on liquids

Abstract

The very large number of states arise in a typical Monte Carlo simulation of a liquid was replaced by a relatively small number of states by discretizing the energy distribution function. We found that the subdominant eigenvalues of transition matrices defined over these states only weakly depend on the number of states used in the representation. Transition matrices defined over distribution functions with 276 states were then used to approximate the true transition matrices underlying the force-bias and Metropolis Monte Carlo algorithms. We examine the influence of limited state-to-state accessibility, and of distortion in the force-bias biasing function, on a variety of properties, most notably the subdominant eigenvalues of the transition matrices and the stochastic characteristics of the developing distribution function. Our results suggest that because of the inevitable presence of both limited accessibility and distortion in the biasing function, the force-biased algorithm with a moderate degree of biasing is best.