On some modified spherical models.
A one parameter family of models is considered which for zero value of the parameter alpha reduces to the familiar spherical model. The models for alpha > 0 have a symmetry close to that of an Ising model. A heuristic discussion of phase transitions in these models leads to the conjecture that, if the spherical model (alpha = 0) exhibits a phase transition, then so do the models with alpha > 0, and that moreover the critical temperature remains the same, at least for sufficiently small alpha. The conjecture is checked on a mean field model.
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