Phase transitions in random-anisotropy magnets

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Abstract
Recursion relations for m-component random-anisotropy magnets on hierarchical lattices are calculated to third order in 1/p, where p is the number of parallel links at each level of the lattice. Setting m=1 gives the Ising spin glass, for which we find the usual ferromagnetic, spin-glass, and ferromagnet–spin-glass fixed points. The results for p=4 suggest that in three dimensions the ferromagnetic critical point is unstable for m=2, resulting in either a first-order transition or an infinite-susceptibility phase. For m=3 ferromagnetism may disappear altogether, at least in the strong anisotropy limit. The spin-glass critical exponents are functions of p, but independent of m.