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 E₀ 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 E₀/J are -1.5075±{}0.0015, -2.229±{}0.003, and -2.543±{}0.002.