Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model

Abstract

The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included. The wetting transition is critical (second order) for any finite ratio of surface coupling J s to bulk coupling J, and turns first order in the limit J s /J → ∞. However, for J s /J 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition displays firstorder character. Surprisingly, in this regime the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.

First-order wedge wetting revisited

“…would be examples of apparent first-order wetting similar to that discussed recently in the literature 33,34 .…”

Classical density functional study of wetting transitions on nanopatterned surfaces

“…In this case, the unbending line appears as a rounded transition. However, recent studies of wetting in 2D systems have shown that, if the underlying mean-field transition is strongly first-order, the asymptotic critical regime is extremely small, and that the wetting transition remains effectively first-order [45,46]. This, we believe, is pertinent to the transverse wetting occurring on the stripe substrate.…”

Wetting Transition of Active Brownian Particles on a Thin Membrane

“…For −1 ≤ cosðθÞ < 0 the system is partially dry, with a drying transition (the limit of extreme hydrophobicity in which the wall favors the gas phase) occurring as cosðθÞ → −1. The attractive strength of wall-fluid interactions determines γ WG and γ WL and hence θ. Wetting and drying transitions can be first order or critical (i.e., continuous) depending on the properties of the wallfluid interactions and the system dimensionality [6][7][8][9][10].…”

“…Dimensionality can greatly affect the character of surface phase transitions. For example, equilibrium wetting is continuous in 2D [8,39] and discontinuous in 3D [10]. To investigate dimensionality effects, we have studied a 3D system of ABPs in an arrangement similar to that of the 2D system described above.…”