Topics in Lattice Statistics: I. Systematics of Multilayer Adsorption Phenomena on Attractive Substrates. I. Dynamical Critical Exponents for the Kinetic Ising Model: a Finite - Hamiltonian Calculation.

This thesis consists of two parts. The first and major part is contained in Chapter I and deals with multilayer adsorption and wetting phenomena on attractive substrates. The second part, contained in Chapter II, is devoted to the study of kinetic Ising models, using finite-size Hamiltonian methods. In Chapter I we give a brief introduction to surface and interfacial thermodynamics, followed by an overview of multilayer adsorption phenomena, such as "layer transitions," "wetting," and "prewetting." We use a mean-field theory to study the systematics of such multilayer adsorption phenomena in a lattice-gas (Ising) model. Though some similar calculations have been done previously, ours is the first to explore the systematics of these phenomena. We also indicate how we expect to be modified by the inclusion of thermal fluctuations that are ignored completely in a mean-field theory. In most of our work we use short -range, attractive substrate potentials; however, we discuss briefly, how long-range, attractive substrate potentials would modify our results. Lastly, we show how the mean -field theory that we use and, in general, mean-field theories of one-dimensionally inhomogeneous systems, may be formulated as area-preserving maps. This formulation is completely equivalent to other formulations of mean-field theory. However, it does offer different insights, which we explore in some detail for the surfaces and interfaces of lattice models. In Chapter II we give a brief introduction to kinetic Ising models. Using a Hamiltonian formulation of the master equation that describes the dynamics of the Ising model, we calculate the dynamical critical exponent z via finite-size methods. These are the first calculations of their kind. In one dimension we find that different transition probabilities give different values for z. We discuss the reason for this "nonuniversality." In two dimensions z still depends on the form of the transition probability. We argue in this case that z should really be universal but that finite-size calculations are not very reliable when the lattices used are very small.