Critical point in the Percus-Yevick theory

Some consequences of the Percus-Yevick theory are studies in the neighborhood of the critical point for adhesive hard spheres and for the 6 potential (truncated at 6σ). It is shown that the Percus-Yevick theory gives rise to classical behavior at the critical point. In particular, it is shown that for the compressibility equation of state the critical exponents γ and δ are 1 and 3, respectively, and for the energy equation of state the critical exponents α and β are 0 and 1/2, respectively. In addition, the behavior of the Percus-Yevick distribution function in the neighborhood of the critical point is examined and it is shown that for the critical isochore the temperature derivative of the distribution function diverges with a critical exponent of 1/2 which is independent of r and that for the critical isotherm the distribution function is a linear function of the density for all r. © 1972 The American Physical Society.