Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

Abstract

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.

17 pages, 5 figures. Review paper to appear in Molecular Physics

References in corpus (7)

• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Critical behavior in colloid-polymer mixtures: theory and simulation
• Liquid-vapor transition from a microscopic theory: Beyond the Maxwell construction
• Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory
• Towards a unification of HRT and SCOZA
• Nonuniversal routes to universality: Critical phenomena in colloidal dispersions

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• Phase transition in a cell fluid model
• First-order phase transition in the framework of the cell fluid model: Regions of chemical potential variation and the corresponding densities
• Universal behavior of soft-core fluids near the threshold of thermodynamic stability
• Uniform quantized electron gas
• Critical region of D-dimensional spins: Extension and analysis of the hierarchical reference theory
• Routes to the density profile and structural inconsistency
• The uniform quantized electron gas revisited
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids