The critical wetting saga: how to draw the correct conclusion

Abstract

A long-standing problem in condensed matter physics concerns the nature ofthe critical wetting phase transition in the Ising model or, more generally, in3D systems with short-ranged forces. This is of fundamental interest because3D corresponds to the upper critical dimension of the transition and it is notclear a priori whether the behaviour of the system will be mean-field-like orfluctuation-dominated. Renormalization group studies of the standard coarse-grainedeffective interfacial Hamiltonian model famously predict strong non-universalcritical exponents which depend on the value of the so-called wetting parameterω. However, these predictions are at odds with extensive Monte Carlo simulations of wettingin the Ising model, due to Binder, Landau and coworkers, which appear to bemore mean-field-like. Further amendments to the interfacial Hamiltonian, whichincluded the presence of a position-dependent stiffness, worsened the problemby paradoxically predicting fluctuation-induced first-order wetting behaviour.Here we show from re-analysis of a microscopic Landau–Ginzburg–Wilson model of 3Dshort-ranged wetting that correlation functions are characterized by two diverging parallellength scales, not one, as previously thought. This has a simple diagrammatic explanationusing a non-local interfacial Hamiltonian and yields a thermodynamically consistent theoryof wetting in keeping with exact sum rules. The non-local model crucially containslong-ranged two-body interfacial interactions, characterized by the new length scale, whichwere missing in earlier treatments. For critical wetting the second length cuts off thespectrum of interfacial fluctuations determining the repulsion from the wall. We show howthis corrects previous renormalization group predictions for fluctuation effects, basedon local interfacial Hamiltonians. In particular, lowering the cut-off leads to asubstantial reduction in the effective value of the wetting parameter controllingthe non-universality and also prevents the transition being driven first-order.Quantitative comparison with the Ising model simulation studies is also made.