Effect of physical cluster formation on the behavior of correlation functions for a fluid system

Physical cluster formation in a fluid system causes a characteristic dependence of the pair correlation function on the distance r between a specific pair of particles at the liquid–vapor critical point. Its dependence deviates from that expressed by the product of a negative power r−1 and a specific function provided by a Taylor series with respect to positive powers of r. The effects of the physical cluster formation can be estimated by representing the pair correlation function as a sum of two correlation functions; these two correlation functions can be provided as exact solutions for two differential equations that result from a system of two integral equations equivalent to the Ornstein–Zernike equation.