Infinite susceptibility phase in planar random-anisotropy magnets

A Monte Carlo algorithm has been used to study the random-anisotropy model with two-component spins on simple cubic lattices, in the strong anisotropy limit. The magnetic susceptibility diverges at a temperature of ${\mathit{T}}_{\mathit{c}}$/J=1.91±0.03, but no singular behavior is observable in the specific heat near ${\mathit{T}}_{\mathit{c}}$. The two-spin correlation function at ${\mathit{T}}_{\mathit{c}}$ is described by a critical exponent η=0.04±0.04. The magnetization of the ground state of a lattice of size L is approximately 1/[0.37 ln(L)+1] per spin. At t=0 the value of ${\mathrm{\eta }}_1$ is -0.34±0.06, which agrees with small-angle neutron-scattering experiments on certain amorphous magnetic alloys.