High-temperature series for random-anisotropy magnets

High-temperature series expansions for thermodynamic functions of random-anisotropy-axis models in the limit of infinite anisotropy are presented, for several choices of the number of spin components, m. In three spatial dimensions there is a divergence of the magnetic susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{M}}$ for m=2. We find ${\mathit{T}}_{\mathit{c}}$/J=1.78\ifmmode\pm\else\textpm\fi{}0.01 on the simple cubic lattice, and on the face-centered cubic lattice, we find ${\mathit{T}}_{\mathit{c}}$/J=4.29\ifmmode\pm\else\textpm\fi{}0.01. There is no divergence of ${\mathrm{\ensuremath{\chi}}}_{\mathit{M}}$ at finite temperature for m\ensuremath{\ge}3 on either lattice. We also give results for simple hypercubic lattices.