Interacting Fermion Theory of the Wandering Domain Walls in the Two-Dimensional Commensurate-Incommensurate System

Abstract

The transfer matrix formalism for an assembly of physisorbed atoms on an anisotropic rectangular lattice is developed. In this formalism, statistical mechanics of the assembly is reduced to a quantum mechanical problem of interacting Fermions in a one-dimensional lattice. The Kosterlitz-Thouless dislocations are neglected. This simplified model is analyzed by means of RPA. A complete phase diagram of this model is given. It is found that there are two commensurate phases C₁ and C₂ and also two incommensurate (or fluid) phases IC₁ and IC₂. Critical phenomena around the phase boundaries are investigated.