Infinite susceptibility phase in planar random-anisotropy magnets

Critical behavior of the three-dimensional random-anisotropy Heisenberg model

We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different anisotropy strengths for each disorder class. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a zero magnetization low-temperature phase. Studying this region using a spin-glass order parameter we have found evidence for a spin-glass phase transition. We have estimated effective critical exponents for the spin-glass phase transition for the different values of the strength of the isotropic disorder, discussing the crossover regime.

Phase transitions in XY models with randomly oriented crystal fields

We obtain a representation of the free energy of an XY model on a fully connected graph with spins subjected to a random crystal field of strength D and with random orientation α. Results are obtained for an arbitrary probability distribution of the disorder using large deviation theory, for any D. We show that the critical temperature is insensitive to the nature and strength of the distribution p(α), for a large family of distributions which includes quadriperiodic distributions, with p(α)=p(α+π/2), which includes the uniform and symmetric bimodal distributions. The specific heat vanishes as temperature T→0 if D is infinite, but approaches a constant if D is finite. We also studied the effect of asymmetry on a bimodal distribution of the orientation of the random crystal field and obtained the phase diagram comprising four phases: a mixed phase (in which spins are canted at angles which depend on the degree of disorder), an x-Ising phase, a y-Ising phase, and a paramagnetic phase, all of which meet at a tetracritical point. The canted mixed phase is present for all finite D, but vanishes when D→∞.