Liquid-State Theory for Critical Phenomena

We have developed a unified theory of classical fluids in the form of a hierarchy of integrodifferential equations for the free energy and direct correlation functions. This theory gives the correct ε=4-d expansion for critical phenomena. The presence of a hard core does not modify the Ising universality class to lowest order in ε. The simplest approximation gives γ=2ν=1.38 in $d=3$. Suitable truncation of the hierarchy gives the correct lowdensity (virial coefficients) and high-density (optimized random phase) limit.