Scaling regimes and functional renormalization for wetting transitions

Abstract

Interface unbinding transitions, such as those arising in wetting phenomena, are studied in d dimensions with general interactions. Three scaling regimes must be distinguished: a mean-field (MF), a weak-fluctuation (WFL), and a strong-fluctuation (SFL) regime. A simple picture clarifies the origin and nature of the different regimes and correctly describes the MF and WFL critical behavior. In the SFL regime, however, this picture fails, as do more elaborate perturbative methods. To overcome this an approximate functional renormalization group is introduced: it acts as a nonlinear map in the space of interaction potentials, V(l), for two interfaces at a separation l. The formulation is exact to first order in V and embodies the correct scaling behavior at a continuous unbinding transition. In the SFL regime, it reveals two nontrivial fixed point potentials, $V_0^{\mathrm{*}}$(l) and $V_c^{\mathrm{*}}$(l), which describe, respectively, the completely delocalized phase and the critical manifold for the unbinding transition. On approaching the upper boundary dimension, $d_u$=3, these fixed points do not coalesce with the standard Gaussian fixed point but, rather, mutually annihilate leaving a line of novel ‘‘drifting’’ fixed points. For d<3, sufficiently long-ranged perturbations cause crossover to the WFL and MF regimes. Thus the functional renormalization-group approach yields a unified description of all scaling regimes.