Critical behavior of modified hypernetted-chain equations. II. Nonuniversal quantities

In a recent paper [P.D. Poll and N. W. Ashcroft, Phys. Rev. A 32, 1722 (1985)], numerical solutions of the modified hypernetted-chain (MHNC) equation were presented for a system near its critical point. The particles in this system were assumed to interact through a double-Yukawa pair potential. For a proposed crossover form of bridge function, universal power-law behavior was found in the isothermal compressibility. On the critical isochore and for a fixed set of parameters defining the form of crossover in the bridge function, we present here results for nonuniversal quantities, specifically the excess internal energy and specific heat per particle. These quantities, together with the isothermal compressibility, critical temperature, and critical density are compared with experimental results for argon. Good agreement is found, particularly when experimental results are scaled with parameters taken from an effective state-dependent pair potential partially incorporating many-body effects in the vicinity of the critical region. The parameters defining the form of cross-over in the bridge function are also varied in order to investigate the effect of thermodynamic inconsistency in the MHNC equation on nonuniversal quantities. It is found essential to include pure hard-sphere behavior in the short-range structure of the bridge function in order to reasonably determine these quantities in the critical region.