Constant-coupling approximation of the exchange-interaction model of ferromagnetism

Abstract

The ferromagnetic-exchange-interaction model is studied by the Oguchi method and the constant-coupling approximation (CCA). The polarization q(T), which describes the ordering of the model, is determined for various spins. The phase transition is first order for all spins S\ensuremath{\ge}1. The transition temperature obtained with the CCA is ${\mathit{kT}}_{\mathit{c}}$/J=2/{lnS(2S-1)-ln[(2S${)}^{\mathrm{\ensuremath{\zeta}}}$-S(2S+1)]}, where \ensuremath{\zeta} depends on the lattice coordination number z and is given by \ensuremath{\zeta}=2(z-1)/z. Both the CCA and the Oguchi method show that the discontinuity of q at ${\mathit{T}}_{\mathit{c}}$ is ${\mathit{q}}_{\mathit{c}}$=(2S-1)/2S, which is exactly the same as the mean-field result.