Fluid phase coexistence and critical behaviour from simulations in the restricted Gibbs ensemble

TL;DR

This paper develops a framework for analyzing fluid phase coexistence and critical behavior using the restricted Gibbs ensemble, providing methods to accurately estimate critical points and coexistence densities from density fluctuations.

Contribution

It introduces a novel approach linking RGE density fluctuations to grand canonical ensemble data, enabling precise critical and coexistence parameter estimation.

Findings

Proposes a method for accurate coexistence density estimation in the sub-critical region.

Identifies an observable for finite-size estimation of critical point parameters.

Develops a finite-size scaling theory for extrapolating to the thermodynamic limit.

Abstract

The symmetrical restricted Gibbs ensemble (RGE) is a version of the Gibbs ensemble in which particles are exchanged between two boxes of fixed equal volumes. It has recently come to prominence because -- when combined with specialized algorithms -- it provides for the study of near-coexistence density fluctuations in highly size-asymmetric binary mixtures. Hitherto, however, a detailed framework for extracting accurate estimates of critical point and coexistence curve parameters from RGE density fluctuations has been lacking. Here we address this problem by exploiting an exact link between the RGE density fluctuations and those of the grand canonical ensemble. In the sub-critical region we propose and test a simple method for obtaining accurate estimates of coexistence densities. In the critical region we identify an observable that serves as a finite system size estimator for the critical point parameters, and present a finite-size scaling theory that allows extrapolation to the thermodynamic limit.