The Freeon Theory of Ferromagnetism

In this section we give the freeon theory of ferromagnetism. As pointed about above ferromagnetism is a second order-phase change which is well-defined by mean-field theory. In Section 6.2 we give the uniform interaction derivation of mean-field theory and in Section 6.3 we compare prediction with observation. 

The uniform interaction (UI) model assumes that the freeon, Heisenberg ferromagnetic exchange interaction is uniform for all pairs in the sample i. e., 

This is the freeon analogue [14] of the spin model of Kittel and Shore [IS]. Since the UI Hamiltonian is the sum over all pairs with a uniform interaction strength it can be expressed in the following form 

I will now compute the most probable value of the freeon quantum number, p by means of the canonical partition function. Here it is finally necessary to acknowledge the existence of the conjugate spin space whose dimension (statistical weight) is 

The most probable value of the freeon quantum number p is given by the condition, 

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The mean-field equation will be derived from two models the uniform interaction model and the Ising model. Neither of the two derivations depend explicitly on spin. They will be applied to the freeon theory of ferromagnetism Section 6 and freeon theory of high-Tc superconductivity in Section 7. 

Note that the undoped cuprate is an antiferromagnet and that doping converts it into a superconductor. We have shown above that antiferromagnetic behavior arises from the z = +1 side of the extended Hiickel-Hubbard spectrum in Fig. 4.1. In the ISB theory the superconducting behavior comes from the z = -1 side of Fig. 4.1 just as does the freeon theory of ferromagnetism. 

The freeon theory of ferromagnetism is based on the negative-U, Hiickel-Hubbard Hamiltonian (NUHH). However the conventional positive-U, Hiickel-Hubbard (PUHH) Hamiltonian employs a positive U which is a measure of the repulsion of a bare pair of electrons on a single site. From whence comes NUHH There are three positions to take with respect to NUHH ... 

In Section 4.4 the freeon ferromagnetic Hamiltonian is used to the develop the freeon theory of spin-waves. 

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