The two-dimensional Ising model

Abstract

In this thesis the equivalence of the two-dimensional critical classical Ising model in the scaling limit without a magnetic field, the (one-dimensional) critical quantum Ising chain in the scaling limit, the free fermion with a Dirac mass term, theM(3, 4) minimal model is reviewed. It is shown that the affine diagonal coset model of E8 (respectively su(2)) describes the critical one dimensional quantum Ising model sightly perturbed with a magnetic field term (respectively an energy density term) from the critical point. Furthermore, the existence of six integrals of motion is proven in the critical quantum Ising chain perturbed with a small magnetic field term from the critical point, and using these conserved quantities, the existence of eight massive particles and their mass ratios are predicted, following a paper of Zamolodchikov. Title: The two dimensional Ising model Author: Sjabbo Schaveling, sjabboschaveling@student.uva.nl, 10001230 Supervisor: prof. dr. E. M. Opdam, prof. dr. B. Nienhuis Second Examiner: Prof. dr. B. Nienhuis Examination date: Februari 29, 2016 Korteweg-de Vries Institute for Mathematics University of Amsterdam Science Park 105-107, 1098 XG Amsterdam http://kdvi.uva.nl