The Ornstein-Zernike equation and critical phenomena in fluids

摘要

It is shown that there are two classes of closure equations for the Ornstein-Zernike (OZ) equation: the analytical equations B=B-(an) type of hyper-netted-chain approximation, Percus-Yevick approximation etc., and the nonanalytical equation B=B-(non), where B-(nan)=B-(RG)+B-(cr); 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 a critical point and other individual features of critical phenomena, and B-(nan) defines known relations between critical exponents. It is shown that a necessary condition for the existence of a nonanalytical solution of the OZ equation is the equality 5-eta=delta(1+eta), where eta and delta are critical exponents, the values of which can change in a narrow interval. It is shown that the transition from analytical solution to nonanalytical solution is accompanied by a step of derivative of pressure. On the phase diagram of fluids the boundaries dividing the area of existence of analytical and nonanalytical solutions are indicated.