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Interface-unbinding transitions, such as those arising in wetting phenomena, are studied in two-dimensional systems with quenched random impurities and general interactions. Three distinct universality classes or scaling regimes are investigated using scaling arguments and extensive transfer-matrix calculations. Both the critical exponents and the critical amplitudes are determined for the weak- and the strong-fluctuation regime. In the borderline case of the intermediate-fluctuation regime, the asymptotic regime is not accessible to numerical simulations. We also find strong evidence for a nontrivial delocalization transition of an interface that is pinned to a line of defects.

Critical and complete wetting transitions are studied in the solid-on-solid limit of the threedimensional Ising model. The surface order parameter and coverage are calculated using Monte Carlo methods for various T > TR (the roughening temperature). The critical behavior is found to be universal but consistent with renormalization-group predictions. We predict that for Tm: (i) the parameter (o^ in the Ising model; this is much less than the previous estimate @^I; (ii) the length scale in the effective interface potential is about twice as large as the Ising bulk correlation length.

We analyze a square-lattice random-bond Ising model using a numerical transfer-matrix technique to test the theory proposed by Lipowsky and Fisher for the complete wetting transition of a wall by one of two phases which coexist in a random medium. The theoretical scaling arguments are checked in detail. The transverse and longitudinal correlation lengths, a h ) and C$h), are found to be related by ~ i ~ ~ with 6=0.65*0.02 as the external field, or chemical potential deviation, h, approaches 0: the theoretical expectation is S , = + The mean wetting layer thickness diverges as l(h)-h-*while&-hvlas h-0with $=vi=^.

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 dl3, 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.

A fluid (or Ising-like) system in contact with a uniformly curved substrate, such as a cylinder or sphere, exhibits a surface phase diagram which is different from that when the substrate is flat. Using both an interface model and a Landau theory that includes surface field and surface coupling enhancement parameters, we find that the effects of curvature may be subsumed into an effective bulk (ordering) field. Complete and critical wetting transitions are thus suppressed. At bulk coexistence, the mean-field phase diagram exhibits curvature-induced prewetting and critical prewetting transitions. In d=3, finite-size effects smear the prewetting transitions that would otherwise take place in cylindrical or spherical geometries. The Landau theory employs a nonanalytic, piecewise parabolic approximation to the usual quartic polynomial in the free-energy functional. This approximation produces a global surface phase diagram with the correct topology, even though it is unsuited for the description of multicritical phenomena, such as wetting tricriticality. Other strengths and weaknesses of the approximation are described.

The approach towards complete wetting is considered for adsorbed liquid layers and for gravity-thinned layers in binary mixtures. These layers are bounded by one or two fluid-fluid interfaces. The thermal fluctuations of those interfaces are studied in the framework of effective interfacial models. Their correlation function C(x) is calculated within the Ornstein-Zernike approximation and by transfer-matrix methods. For large distances x, C(x)\ensuremath{\propto}exp(-x/${\ensuremath{\xi}}_{?}$). Due to the divergence of the correlation length ${\ensuremath{\xi}}_{?}$, complete wetting can be regarded as a critical phenomenon. Two different scaling regimes have to be distinguished depending on the nature of the long-ranged forces and on the dimensionality. In the mean-field regime, the critical exponents depend on the long-ranged forces. In the fluctuation-dominated regime, they depend only on the dimensionality. It is also shown that these critical effects are characterized by one superuniversal feature: The critical exponent \ensuremath{\eta} which governs the decay of the correlation function C(x) for x\ensuremath{\ll}${\ensuremath{\xi}}_{?}$ is zero both in the mean-field and in the fluctuation-dominated regime. The result \ensuremath{\eta}=0 is expected to be valid for all types of wetting transitions. The experimental work which has focused on the thickness of the wetting layer is briefly reviewed. Furthermore, two types of experiments are proposed by which the correlation length ${\ensuremath{\xi}}_{?}$ could be observed: it should show up both in the intensity of the small-angle scattering of light from the interfaces and in experiments which measure the dispersion relation of the capillary waves. This relation is found to be ${\ensuremath{\omega}}^{2}$(q)\ensuremath{\propto}q(${q}^{2}$+${\ensuremath{\xi}}_{?}^{\mathrm{\ensuremath{-}}2}$), where \ensuremath{\omega} and q are the frequency and the wave number of such waves. It is also suggested that the regime of critical wetting could be obtained in binary mixtures by the addition of impurities.

The pinning of a domain wall by an external potential is studied in the solid-on-solid limit of the $d$-dimensional inhomogeneous Ising ferromagnet. Analyzing a field theoretic generalization of this model, we show that, if the pinning potential is applied near the edge of the system, a localization-delocalization transition occurs for all $\frac{5}{3}ldl~3$. Results for singular behavior of the surface tension, correlation length, and interface moments are derived.

Universality classes and critical exponents for the wetting transition in two dimensions are determined with the use of a continuum planar solid-on-solid model. Effective substrate potentials BU( f)

Semi-infinite systems are considered which give rise to a delocalization transition of the interface between two coexisting phases. Since the interface position becomes a zero mode at the transition, interface fluctuations invalidate mean-field theory for space dimension $dl~3$. An effective field-theoretic model for this zero mode is obtained via the collective-coordinate method. Results for a simplified version of this model in $d=2$ and in $d=3$ are reported.

Semi-infinite systems are considered which undergo a first-order transition. The global phase diagram is discussed within the framework of Landau theory. Several types of phase transitions are found. At some of these transitions, critical surface phenomena occur since a variety of surface exponents may be defined although there are no bulk exponents.

The relationship between surface wetting transitions and surface-induced disorder (SID) transitions is studied. The correspondence between the scaling variables at these two types of interface delocalization transitions is derived and the connection between the scaling laws is made explicit. This wetting-SID correspondence is then used to obtain a number of new results. SID transitions are shown to correspond to special points in more general interface delocalization phase diagrams and it is argued that the SID transition is always continuous in d =2. Exact results for the surface exponents are obtained in this case. New higher-order multicritical wetting phenomena are also predicted and the scaling behavior of local surface quantities at the wetting transition is discussed in detail.

Lamellar phases of lyotropic liquid crystals can be swollen by addition of solvent. Such a process, which leads to a strong increase of the mean interlamellar separation /, can be viewed as a phase transition, termed complete unbinding. Starting from the microscopic interaction for a pair of lamellae, we derive an effective model for the multilayer phase. We predict a power-law increase of /, and show that the system exhibits quasi-long-range translational order characterized by an exponent X,,, which is either universal or, for sufficiently long-range repulsive interactions, depends on molecular details.

Interface delocalization transitions are studied for slabs and strips of linear dimension L. For large L , the shift of the transition temperature is found to be proportional to l / L . This implies that the continuous behavior predicted for various surface quantities in a semi-infinite geometry becomes weakly discontinuous for large but finite L. The consequences for new experiments and computer simulations on threeand two-dimensional systems are discussed