Absence of a stiffness instability for a model critical-wetting transition in three dimensions

Abstract

We have tested the generality of the stiffness instability mechanism recently proposed by Fisher and Jin (1993) for the critical wetting phase transition in three-dimensional systems with short-ranged forces. We extend the analysis of Fisher and Jin to a class of Aukrust-Hauge type models and find that the stiffness instability is specific to the case where the unrenormalized transition is precisely second order (i.e where the mean-field specific heat critical exponent is precisely zero). A linear functional renormalization-group analysis of this Aukrust-Hauge class of models yields exactly the same dramatic fluctuation-induced non-universal critical exponents that have previously been predicted. We conclude by considering possible implications of this result on future Ising model simulations and on the basis of this propose a numerical test for the validity of existing renormalization-group analyses of continuum effective interfacial Hamiltonians.