Irrelevance of bulk symmetry to critical wetting

Abstract

We consider a q-state Potts model below its critical temperature, which is in contact with a wall. The bulk is in one of the q phases while the wall favors one of the others. We show that if the critical wetting exponents are universal, independent of the wall, then they are superuniversal, independent of q and thus of the bulk symmetry. The order parameter of the wetting transition can be taken to be of one component, the thickness of the wetting layer. Although this derivation is within mean-field theory, we believe the result to be true in all dimensions.