Liquid-vapor transition from a microscopic theory: beyond the Maxwell construction.

A smooth cutoff formulation of the hierarchical reference theory (HRT) is developed and applied to a Yukawa fluid. The HRT equations are derived and numerically solved leading to the expected renormalization group structure in the critical region, nonclassical critical exponents and scaling laws, a convex free energy in the whole phase diagram (including the two-phase region), finite compressibility at coexistence, together with a fully satisfactory comparison with available numerical simulations. This theory, which also guarantees the correct short range behavior of two body correlations, represents a major improvement over the existing liquid-state theories.