Fluid Critical Points from Simulations: the Bruce-Wilding method and Yang-Yang anomalies

TL;DR

This paper critically examines the Bruce-Wilding method for estimating critical points in nonsymmetric fluids, revealing its strengths and limitations, especially regarding pressure mixing effects and the lack of a general theoretical foundation.

Contribution

The paper provides a systematic implementation of the Bruce-Wilding method and analyzes the impact of pressure mixing on critical point estimations.

Findings

The Bruce-Wilding method effectively estimates critical points for Ising-type systems.

Pressure mixing alters the critical density estimator's behavior.

The method's success relies on a fortunate cancellation of correction contributions.

Abstract

A critique is presented of the frequently used Bruce-Wilding (BW) mixed-field scaling method for estimating the critical points of nonsymmetric model fluids from grand canonical simulation data. An explicit, systematic technique for implementing this method is set out thereby revealing clearly a fortunate, close cancelation of contributions from the leading correction- to-scaling and thermal scaling functions that makes the method effective for Ising-type systems but which lacks a general theoretical basis. Pressure mixing is considered in this work which modifies the leading behavior of the critical density estimator while the critical temperature estimator maintains the leading behavior asserted by BW.