A fieldtheoretical 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 fieldtheoretical formalism. It is based on applying the complex HubbardStratonovich transformation to the canonical and grandcanonical 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 grandcanonical ensemble using a system of particles interacting through a purely repulsive Gaussian pair potential in a broad range of external parameters. In the grandcanonical case this technique represents an alternative to standard grandcanonical 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 August 2002
 DOI:
 10.1063/1.1488587
 Bibcode:
 2002JChPh.117.3027B
 Keywords:

 statistical mechanics;
 Monte Carlo methods;
 classical field theory;
 Classical Mechanics;
 Computerized Simulation;
 Field Theory (Physics);
 Monte Carlo Method;
 Statistical Mechanics;
 05.20.Gg;
 61.20.Ja;
 Physics (General);
 Classical ensemble theory;
 Computer simulation of liquid structure