The effect of a local anisotropy of random orientation on a ferromagnetic phase transition is studied. To this end, a model of a random anisotropy magnet is analysed by means of a field theoretical renormalization group approach. The one-loop result of Aharony about the absence of a 2nd order phase transition for isotropic distribution of random anisotropy axis at space dimension d < 4 is corroborated.

The critical behaviour of an m -vector model with a local anisotropy axis of random orientation is studied within the field-theoretical renormalization group approach for cubic distribution of anisotropy axis. Expressions for the renormalization group functions are calculated up to the two-loop order and investigated both by an ε = 4 − d expansion and directly at space dimension d = 3 by means of the Padé-Borel resummation. One accessible stable fixed point indicating a 2nd order ferromagnetic phase transition with dilute Ising-like critical exponents is obtained.

We study the purely relaxational critical dynamics with non-conserved order parameter (model A critical dynamics) for three-dimensional magnets with disorder in a form of the random anisotropy axis. For the random axis anisotropic distribution, the static asymptotic critical behaviour coincides with that of random site Ising systems. Therefore the asymptotic critical dynamics is governed by the dynamical exponent of the random Ising model. However, the disorder effects considerably the dynamical behaviour in the non-asymptotic regime. We perform a field-theoretical renormalization group analysis within the minimal subtraction scheme in two-loop approximation to investigate asymptotic and effective critical dynamics of random anisotropy systems. The results demonstrate the non-monotonic behaviour of the dynamical effective critical exponent z eff .

The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics, the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities, the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the measurable electric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the time scales of the order parameter and the gauge field are different.

The paper contains materials of the discussion concerning phase transitions and critical phenomena which took place during the Workshop on modern problems of soft matter theory (August 27-31, 2000, Lviv, Ukraine).