Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Abstract

We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and XY Z model, which is simple to apply for calculation of various correlation functions. We calculate the partition function of 2DIM and XY model within the developed framework. Determinant representation of spin-spin correlation functions is derived using fermionic realization for the Boltzmann weights. The approach also allows formulation of the partition function of 2DIM in the presence of an external magnetic field.