A field-theoretical approach to simulation in the classical canonical and grand canonical ensemble

Abstract

In this paper we present a new approach to simulation methods for classical statistical mechanics relying on a field-theoretical formalism. It is based on applying the complex Hubbard–Stratonovich transformation to the canonical and grand-canonical partition function, which allows one to reexpress their particle representation in terms of a functional integral over a fluctuating auxiliary field. The thermodynamic averages from the resulting field representations can then be calculated with a conventional Monte Carlo algorithm. We explored the applicability of the auxiliary field methodology for both the canonical and grand-canonical ensemble using a system of particles interacting through a purely repulsive Gaussian pair potential in a broad range of external parameters. In the grand-canonical case this technique represents an alternative to standard grand-canonical Monte Carlo methods. Generally providing a framework for simulating classical particle systems within a continuum formalism can be useful for multiscale modeling where the field or continuum description naturally appears within quantum mechanics on smaller length scales and within classical mechanics on larger ones.