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

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 that lacks a general theoretical basis. The BW approach does not allow for pressure mixing in the scaling fields, which is essential for representing a Yang−Yang anomaly (namely, the divergence at criticality of the second temperature derivative, (d2μσ/dT 2), of the chemical potential μσ(T) on the phase boundary), but such behavior must be expected in realistic models. We show that allowance for pressure mixing does not alter the leading dependence of the critical temperature estimator, Tc(L), on the linear size, L, of the simulation box: th...