A Bridge between the Microscopic Interaction Potentials in a Fluid and Effective Long-wavelength Hamiltonians

Abstract

The asymptotic and preasymptotic critical behavior of the three-dimensional Ising universality class, which includes easy axis magnets and fluids, is believed to be described by effective ψ 4 scalar field theory with suitable, non-universal, coupling constants. Universal properties do not depend on the specific values of these coupling constants but this is not so for the non-universal properties. Here we show that the coupling constants dependence on microscopic potentials can be studied using the Hierarchical Reference Theory (HRT), which implements the basic ideas of Wilson momentum renormalization group to microscopic Hamiltonians. We discuss the application of this method to two different microscopic models of intermolecular potential of a simple fluid and to the Ising model. Also the wetting phase transition in a fluid near a wall is described by an effective Hamiltonian. This Hamiltonian contains an effective interfacial potential, which describes the effective interaction of interface with the wall. Here we show how to extend the HRT formalism to inhomogeneous system and how, in such theory, we can extract the interfacial quantities and study their behavior.