3D Short-Range Wetting and Nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.

Figure 1

Wetting diagram and its algebraic expression.

Figure 2

Effective value of the wetting parameter as a function of the wetting thickness. Simulations of the discretized local (triangles) and nonlocal (circles) interfacial models were performed on an $L\times L$ grid. Here $L$ is measured in units of $3.1623/\kappa$ [4]. The thick lines are guides for the eye. The continuous and dashed lines are predictions of the continuum approximation (18) for different $\Lambda$. The value of ${\omega }_{\mathrm{eff}}$ obtained from Ising model simulations [3] is also shown (square).