THEORY OF PHASE-TRANSITIONS IN 2-DIMENSIONAL SYSTEMS

A detailed description of phase transitions in two dimensions is prese nted based on the two-dimensional classical XY model. After describing the basic physics of topological ordering, the starting model Hamilto nian is constructed for a detailed study. Following this, a direct spa ce renormalization programme is presented. The obtained phase transiti on is analysed in detail based on the scaling equations. The systemati c renormalization group calculation up to third order based on field-t heoretical techniques is also presented. The notion of topological exc itations from the viewpoint of the dual model is analysed in detail. T he D > 2 cases are analysed through the three-dimensional XY model and layered systems. This article is pedagogical in nature and is intende d to be accessible to any graduate student or physicist who is not an expert in this field.