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 .

A novel approach is developed for computer simulation studies of dynamical properties of spin liquids. It is based on the Liouville operator formalism of Hamiltonian dynamics in conjunction with Suzuki-Trotter-like decompositions of exponential propagators. As a result, a whole set of symplectic time-reversible algorithms has been introduced for numerical integration of the equations of motion at the presence of both translational and spin degrees of freedom. It is shown that these algorithms can be used in actual simulations with much larger time steps than those inherent in standard predictor-corrector schemes. This has allowed one to perform direct quantitative measurements for spin-spin, spin-density and density-density dynamical structure factors of a Heisenberg ferrofluid model for the first time. It was established that like pure liquids the density spectrum can be expressed in terms of heat and sound modes, whereas like spin lattices in the ferromagnetic phase there exists one primary spin in the shape of spinspin dynamic structure factors describing the longitudinal and transverse spin fluctuations. As it was predicted in our previous paper [Mryglod I., Folk R. et al., Physica A277 (2000) 389] we found also that a secondary wave peak appears additionally in the longitudinal spin-spin dynamic structure factor. The frequency position of this peak coincides entirely with that for a sound mode reflecting the effect of the liquid subsystem on spin dynamics. The possibility of longitudinal spin wave propagation in magnetic liquids at sound frequency can be considered as a new effect which has yet to be tested experimentally.

The phases of a magnetic fluid in an external field are considered. As model systems we take an ideal (hard core) gas with Ising interaction and a van der Waals gas with additional Heisenberg interaction. In mean field approximation various phases and critical points are identified. For appropriate values of the ratio of the magnetic to the non-magnetic interactions there exist multicritical points like tricritical points and critical end points. For the ideal Ising fluid we calculate the line of wing critical points analytically and prove classical tricritical behaviour. In the van der Waals case wing critical points and the gas-liquid critical point may coexist. The corresponding phase diagrams in (p, t, h) -space are shown.