Theory of Critical Fluctuations and Singularities

(1) In the previous lectures the behavior of the macroscopic thermodynamic functions of systems in equilibrium near critical points has been discussed. Notations for the various exponents describing the critical singularities have been introduced and the connections between them have been described [l]. In this talk we enter the microscopic domain by studying the correlation functions and their relation, on the one hand, to the thermodynamic properties and, on the other hand, to the phenomena of critical fluctuations as observed through critical opalescence and scattering experiments. Perhaps the most important correlation function is the net pair correlation function, namely, in a fluid system