Fluid coexistence close to criticality: scaling algorithms for precise simulation

A novel algorithm is presented that yields precise estimates of coexisting liquid and gas densities, p(+/-)(T), from grand canonical Monte Carlo simulations of model fluids near criticality. The algorithm utilizes data for the isothermal minima of the moment ratio Q(L)(T; (L)) equivalent to < m(2)>(2)(L)/< m(4)>(L) in L x (...) x L boxes, where m = rho - (L). When L -> infinity the minima, Q(m)(+/-)(T; L), tend to zero while their locations, rho(+/-)(m)(T; L), approach rho(+)(T) and rho(-)(T). Finite-size scaling relates the ratio gamma = (rho(+)(m) - rho(-)(m))/Delta rho infinity(T) universally to (1)/(2)(Q(m)(+) + Q(m)(-)),where Delta rho infinity = rho(+)(T) - rho(-)(T) is the desired width of the coexistence curve. Utilizing the exact limiting (L -> infinity) form, the corresponding scaling function can be generated in recursive steps by fitting overlapping data for three or more box sizes, L-1, L-2,..., L-n. Starting at a T-0 sufficiently far below T-c and suitably choosing intervals Delta T-j = Tj+1 - T-j > 0 yields Delta rho infinity (T-j) and precisely locates T-c. The algorithm has been applied to simulation data for a hard-core square-well fluid and the restricted primitive model electrolyte for sizes up to L/a = 8-12 (where a is the hard-core diameter): the coexistence curves can be computed to a precision of +/- 1-2% of rho(c) up to vertical bar T - T-c vertical bar/T-c = 10(-4) and 10(-3), respectively. Universality of the scaling functions and the exponent beta is verified and the (T-c, rho(c)) estimates confirm previous values based on data from above T-c. The algorithm extends directly to calculating the diameter, rho(diam)(T) equivalent to (1)/(2)(rho(+) + rho(-)), and can lead to estimates of the Yang-Yang ratio. Furthermore, a new, explicit approximant for the basic scaling function gamma permits straightforward estimates of Delta rho infinity(T) from limited Q-data when Ising-type criticality may be assumed. (c) 2005 Elsevier B.V. All rights reserved.