Bosonization of the 2-D Ising model and correlation functions

Abstract

The critical two dimensional Ising model is studied by using the properties derived from Conformal Invariance. Self-duality is reflected as a double-generacy of the ground state in the periodic (Ramond) sector. The Ising model is doubled obtaining an Ashkin-Teller model at the decoupling point. Using bosonization this model is mapped onto the Gaussian model at a particular value of the temperature. The product of order (or disorder) operators of the two Ising models as well as the spinor and energy operators of each Ising model are expressed as combinations of spin-wave and vortex operators of the Gaussian model. We compute several correlation functions of order, disorder, spinor, and energy operators and show that the operator product expansions predicted by Conformal Invariance are satisfied. We give a simple prescription to compute any N-point (mixed) correlation function at criticality. A bosonized form of the continuum limit of the transfer matrix for the critical Ising model is given. A proof is provided for the identifications and conjectures of Kadanoff and Brown.