Critical point scaling in the Percus-Yevick equation

It is pointed out that the solution of the Percus-Yevick equation for sticky hard spheres, obtained by Baxter, scales exactly in the critical region with classical, Van der Waals exponents. However, even though the correlation functions achieve the Ornstein-Zernike forms, the scaling functions for the equation of state are not classical: in particular, the usual asymptotic gas-liquid symmetry is strongly violated; there is a spinodal curve only for the liquid phase; the specific heat, Cv, on the critical isochore is logarithmically divergent, and, quite unphysically, Cv is also logarithmically divergent on the critical isotherm above the critical density. Finally, comparison with numerical calculations for Lennard-Jones interactions suggests that the scaling functions are, in general, nonuniversal for the PY equation.