Derivation of Landau Theories and Lattice Mean-field Theories For Surface and Wetting Phenomena, From Semi-infinite Ising-models

The phenomenological aspects of surface and interfacial phenomena such as wetting phase transitions are commonly studied using the classification scheme provided by the Landau theory. Although this approach is very meaningful, it is also important to establish a firm connection between the phenomenology and the microscopic models of statistical mechanics. This is true, especially in view of the remarkable sensitivity of wetting phenomena to the details of the substrate-adsorbate interactions. We study such connections and derive a variety of lattice mean-field theories, which make a bridge between the Landau theory and the semi-infinite Ising model with a surface. We discuss standard mean-field approximations (MFA) and improvements thereof, renormalization group techniques, reaction-field approximations, and cluster variation methods. We pay special attention to the derivation of the newly introduced triplet surface field h3 in the Landau theory for wetting.