Characteristics of 2D lattice models from fermionic realization: Ising and $XYZ$ models

TL;DR

This paper introduces a fermionic field theoretical approach to analyze 2D lattice models like the Ising and XYZ models, enabling efficient calculation of correlation functions and partition functions, including in external magnetic fields.

Contribution

The paper presents a novel fermionic realization method for 2D lattice models, simplifying the computation of correlation functions and partition functions.

Findings

Derived determinant representation of spin-spin correlation functions.

Calculated partition functions for 2D Ising and XY models.

Extended the approach to models with external magnetic fields.

Abstract

We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and $XYZ$ 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.