The Trouble with Critical Wetting

A long-standing problem in condensed-matter physics concerns the nature of the critical wetting transition in three-dimensional systems with short-ranged forces. The controversy focused originally on the discrepancy between predictions of strongly non-universal critical effects, based on renormalization group analysis of an interfacial Hamiltonian, and Monte Carlo studies of wetting in the 3D Ising model, which are instead broadly consistent with mean-field expectations. This gulf between theory and simulation was widened further by subsequent refinements of the interfacial model which appeared to show that fluctuations should necessarily drive the transition first-order. This prediction is in qualitative disagreement with the simulation studies and would radically alter the anticipated structure of the global surface phase diagram. We review recent progress made towards overcoming these problems using a new non-local interfacial Hamiltonian. This model, which may be derived systematically from a more microscopic theory and also applied to wetting at structured (non-planar) substrates such as wedges, allows for the presence of two-body interfacial interactions in the wetting layer. These are characterised by an additional diverging coherence length, missing in previous descriptions of wetting. This serves to cut-off the spectrum of interfacial fluctuations that describe the repulsion of the interface from the wall which, in turn, slows down the onset of critical effects (non-universality) and explains why the transition is not driven first-order, therefore preserving the structure of the global surface phase diagram.