We will devote Chapter 1 to a short review of traditional approaches to interfacial phenomena. This starts with an overview on phenomenological descriptions and terminates with a discussion on mean field theories of interfaces. In Chapter 2 we recall some essential notions of scattering theory in two dimensions on which we will rely in the rest of the thesis. In Chapter 3 we will pose the basis of the exact field-theoretic approach to phase separation in two dimensions. In particular, we will develop the formalism for the study of interfaces in a strip geometry. Drops on a flat substrate and the corresponding wetting transition will be discussed in Chapter 4. In Chapter 5 we will analyze phase separation in presence of a wedge-shaped substrate and its field-theoretical implications.
The exposition will cover phase separation both with and without the occurrence of intermediate phases. These two regimes will be discussed in detail for the strip, half-plane and wedge geometries. Our study is based on universal properties of the scaling limit and accounts exactly for the properties of the different universality classes.
The field-theoretical approach to near-critical behavior does not exhaust its applications to interfacial phenomena. We will conclude in Chapter 6 with a further application in which we will consider the thermal Casimir e\u21b5ect, i.e. the analogue of the quantum Casimir e\u21b5ect for statistical systems near criticality. We will show how bulk and boundary e\u21b5ects, jointly with the symmetry of boundary conditions, play a role in the determination of the long-distance decay of the Casimir force
