Statistical theory of critical phenomena in fluids

Abstract

We show that there are two classes of the closure equations for the Ornstein-Zernike equation: The analytical equations for the bridge functional B=B;{(an)} like hypernetted-chain approximation, Percus-Yevick approximation, etc., and nonanalytic equation B=B;{(nan)} , where B;{(nan)}=B;{(rg)}+B;{(cr)} and B;{(rg)} is the regular (analytical) component of the bridge functional, and B;{(cr)} is the critical (nonanalytical) component of B;{(nan)} . The closure equation B;{(an)} defines coordinates of the critical point and other individual features of critical phenomena, and B;{(nan)} defines all the known relations between critical exponents. It is shown, that the necessary condition for existence of the nonanalytic solution of the OZ equation is the equality 5-eta=delta(1+eta) , where eta,delta are the critical exponents, values of which can change in a narrow interval. We also show that the transition from the analytical solution to the nonanalytic one is accompanied by a break of the pressure derivative. The boundaries between the areas, where each of these solutions exists, are indicated on the phase diagram.