An Exactly Soluble Model Showing Ferromagnetism

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Abstract
A Hamiltonian of a one-dimensional Heisenberg model with ferromagnetic interaction is expressed in terms of fermion operators, and renormalized linked cluster expansion has been carried out. It is shown that the approximation leads to ferromagnetic behaviors similar to the molecular field approximation. A model for which the second- and higher-order terms vanish is presented and regarded as an example of quantum-mechanical systems that shows ferromagnetism rigorously. It is also noted that the model is very much like the Husimi-Temperley model or the van der Waals gas with respect to a long-range character of interaction and the vanishing of higher-order terms.