Low-temperature behavior of random-anisotropy magnets

An improved computer annealing algorithm has been used to study the low-energy states of magnets with strong random anisotropy on simple-cubic lattices. For classical Heisenberg spins with isotropically random uniaxial anisotropy, the ferromagnetic correlations at T=0 can be described by a scaling exponent η of about 0.2 and a correlation length of about 10 lattice units. The ground-state energy ${\mathit{E}}_0$ is (-1.118±0.003)J. For XY spins with random p-fold anisotropy, the ground states are ferromagnetic, with magnetizations of 0.45±0.02, 0.715±0.015, and 0.843±0.006, for p=2, 3, and 4, respectively, and the values of ${\mathit{E}}_0$/J are -1.5075±0.0015, -2.229±0.003, and -2.543±0.002.