Long Range Order in Random Anisotropy Magnets

High temperature series for the magnetic susceptibility, χ, of random anisotropy axis models in the limit of infinite anisotropy are presented, for two choices of the number of spin components, m. For m=2, we find T c =1.78 J on the simple cubic lattice, and on the face‐centered cubic lattice we find T c =4.29 J. There is no divergence of χ at finite temperature for m=3 on either lattice. For the four‐dimensional hypercubic lattice, we find finite temperature divergences of χ for both m=2 and m=3.