Bose-Einstein Lattice Gases Equivalent to the Heisenberg Model of Ferro-, Antiferro- and Ferri-Magnetism

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Abstract
The Hamiltonian are presented which are equivalent to the Heisenberg model of ferro-, antiferro- and ferri-magnetism and which have the form of finite power series of the Bose operators. A technique for calculations of partition function for a system with such a Hamiltonian that contains a term of infinite potential is presented and discussed in connection with the theories of a ferromagnetic spin system by Van Kranendonk and Dyson.