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Journal of Physics A Mathematical and General

Generalised XY model

A. I. Solomon, W Montgomery

Published Aug 1, 1978• 2 citations
Publisher

Abstract

The methods of Lie algebras are used to construct and solve a generalisation of the XY model.
DOI
10.1088/0305-4470/11/8/022

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An algebraic method of spin operators was developed by Jha and Valatin to solve (a) the Hamiltonian of the isotropic and anisotropic xy model in a one-dimensional lattice of N spin 1/2 particles and (b) the partition function of the Ising model in the absence of magnetic field in two dimensions. The pair of fermion operators used to explain BCS theory in superconductivity were shown to be related to a set of spin operators of Jha and Valatin in a very simple way. Onsager’s Lie algebra for diagonalizing the partition function of the Ising model was found to be included within the said commutator algebra of the spin operators. The structure constants of the algebra are so simple as to allow the entire algebra to be casted in one general commutator equation. In the present paper, the author presents the proof of a general equation from which all sets of commutator relationships existing among the elements of the algebra directly follow.