Abstract
A systematic study of properties of a set of operators leads to a new approach to solve the XY model. The algebraic solution refers only to a subalgebra of spin operators. Through the connection with the algebra of related fermion operators is apparent, these need not be referred to. As a by-product, Onsager's method for the Ising model results in a very simple form, and its relationship to the approach of Schultz, Mattis and Lieb (1961) becomes apparent.
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