Interface Hamiltonian with a position-dependent stiffness: A nonlinear functional renormalization group study

Abstract

A detailed study of the wetting behavior predicted from an effective interfacial Hamiltonian approach which allows for a position-dependent stiffness coefficient is given. A nonlinear functional renormalization group scheme is introduced enabling earlier studies to be extended into general dimensions $1<d<~3$ while permitting a semiquantitative numerical analysis. We find that the prediction of Fisher and Jin of a bare critical wetting transition being driven fluctuation-induced first order can occur for dimensions $d>{d}_{c}\ensuremath{\approx}2.41$ while at lower $d$ the transition remains critical. For $d>{d}_{c}$ first-order wetting is found if the wetting parameter $\ensuremath{\omega}(T)$ is less than a tricritical value ${\ensuremath{\omega}}_{t}(T).$ Importantly in three dimensions numerical analysis reveals ${\ensuremath{\omega}}_{t}>\ensuremath{\omega}$ thus clearly supporting the premise that the wetting transition in this case is indeed first order. We focus especially on demonstrating the robustness of this result under variation of the stiffness strength and renormalization group rescaling parameter.