A microscopic approach to critical phenomena at interfaces: an application to complete wetting in the Ising model

TL;DR

This paper extends the Hierarchical Reference Theory (HRT) to inhomogeneous systems, specifically analyzing complete wetting in the 3D Ising model, providing insights into critical phenomena and non-universal quantities without coarse graining.

Contribution

The authors develop an HRT formalism for inhomogeneous systems and apply it to study wetting transitions in the Ising model, connecting RG equations with microscopic Hamiltonians.

Findings

HRT reproduces RG critical behavior near wetting transition.

The method captures non-universal quantities without coarse graining.

Numerical results agree with Monte Carlo simulations.

Abstract

We study how the formalism of the Hierarchical Reference Theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid state theory which implements the basic ideas of Wilson momentum shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and non-classical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the non universal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.