Yang-Yang anomalies and coexistence diameters: simulation of asymmetric fluids

A general method for estimating the Yang-Yang ratio, R(mu) , of a model fluid via Monte Carlo simulations is presented on the basis of data for a hard-core square-well (HCSW) fluid and the restricted primitive model (RPM) electrolyte. The isothermal minima of Q(L)(triple bond)2L/L scaling are evaluated at T(c) in an LxLxL box where m=rho-L is the density fluctuation. The "complete" finite-size scaling theory for the Q(+/-)(min) (T(c);L) incorporates pressure mixing in the scaling fields, thereby allowing for a Yang-Yang anomaly. It yields a dominant term in the asymmetry, Q(+)(min)-Q(-)(min) , varying as L(-beta/nu) with an amplitude proportional to the crucial pressure-mixing coefficient, j(2) . The reliably known critical order-parameter distribution for (d=3) Ising systems then enables one to estimate j(2) , thereby yielding R(mu) , from the Q minima together with information on the nonuniversal amplitudes for the order parameter and the susceptibility. The detailed analysis needed to estimate j(2) for an HCSW fluid and the RPM is presented. Furthermore, the Q-minima below T(c) can also provide the coexistence-curve diameters, rho(diam) (T) (triple bond)1/2 (rho(+) + rho(-)) , very close to T(c) for both models: here rho +/-(T) are the densities of the coexisting liquid and gas phases. The recently developed recursive scaling algorithm for Deltarho(infinity) (T) (triple bond)rho(+)-rho(-) is adapted to investigate the corresponding universal scaling functions. The two extremal forms of these scaling functions are computed with the aid of the exactly soluble decorated lattice-gas model. The critical densities for the RPM and HCSW fluid found via this route are consistent with previous estimates obtained from the data above T(c) ; the magnitudes of the |T- T(c)|(2beta) and |T- T(c)|(1-alpha) corrections to rho(diam)(T) are estimated.