The two-dimensional Ising-model on Lattices with Trivial Homotopy Group

Abstract

Contents 1 Introduction 5 2 Thermodynamics, Spin Models and QFT 7 2.1 Basic Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Spin Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Phenomenology of a 2 nd Order Phase Transition . . . . . . . . . 10 2.4 The Relation to Quantum Field Theory . . . . . . . . . . . . . . 12 3 The Two Dimensional Ising-Model 15 3.1 The One Dimensional Ising-Model . . . . . . . . . . . . . . . . . 15 3.2 The Onsager Solution of the Two Dimensional Ising Model . . . 18 4 Boundary Conditions and Finite Size Effects 23 4.1 Finite Size Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 Shift of the Pseudocritical Coupling due to Boundary Effects . . 25 5 Lattice Geometry 27 5.1 Lattice Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Spherical Geometry . . . . . . . . . . . . . . . . . . . . . . .