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

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.

18 pages, RevTex, 2 figures, extended the appraoch to the XYZ model, the published version

References in corpus (3)

• Spin matrix elements in 2D Ising model on the finite lattice
• Thermodynamic Bethe Ansatz for the Spin-1/2 Staggered XXZ- Model
• An Integrable Model with non-reducible three particle R-Matrix

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• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
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• The Yang-Baxter integrability of the critical Ising chain
• New series of multi-parametric solutions to GYBE: quantum gates and integrability