Critical properties of random anisotropy magnets

The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.Comment: 41 pages, 10 figure