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

Abstract

A smooth cut-off 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, non classical 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.

4 pages, 5 figures

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• The smooth cut-off Hierarchical Reference Theory of fluids
• Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
• Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory
• An investigation of the SCOZA for narrow square-well potentials and in the sticky limit
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• Exact Renormalization Group : A New Method for Blocking the Action
• Critical region of D-dimensional spins: Extension and analysis of the hierarchical reference theory
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids