Critical dimension and 1/D expansion for the random anisotropy axis model

Overview & Synopsis

We show that the upper critical dimension for the random anisotropy model of amorphous magnets is four as in the case of the pure ferromagnetic model. We then study the phase transition in this model in the framework of the 1/D expansion (where D is the dimension of space). While the leading term for D → oo does not depend on the anisotropy coupling, the 1/D and 1/D2 corrections decrease the transition temperature between the disordered and the ferromagnetic phase.