Theory of the Ising Ferromagnet Using the Green Function Method

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Abstract
The Green function method is applied to the Ising model of ferromagnetism. It is essential in this paper that we have solved the equations for the Green functions in terms of the correlation functions without using the approximation of decoupling the Green functions as is usually done. Although we get several rigorous relations between the many-spin correlation functions, we do not succeed in solving for the correlation functions, except in the case of a linear chain. We introduce the approximation of eliminating some of the correlation functions using the high temperature expansion, so as to reduce the number of the independent correlation functions. The Curie points of a square lattice and a simple cubic lattice are calculated.

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