The critical region in the Percus–Yevick approximation. A numerical study for a Lennard-Jones potential

The Percus–Yevick equation is numerically solved by using the compressibility equation of state, and its behavior near the critical point is analyzed. We have used a Lennard-Jones potential without truncation, assuming an asymptotic form for the direct correlation function. The results show that the equation of state in the critical region has the same structure as the one obtained from the van der Waals equation. Then, the classical values of the critical exponents are obtained. Furthermore, the critical isotherm, the coexistence curve, and the spinodal curve are symmetrical around the critical point. Thus, the nonclassical behavior of the Percus–Yevick equation seems to be restricted to a certain class of interaction potentials.