Dudka M. Critical properties of magnets: Influence of structural disorder, anisotropy, frustrations

The thesis concerns the study of static and dynamic critical properties of magnets involving realistic features, such as structural disorder, anisotropy, frustrations, which modify O(n)-symmetry of field theory characterizing idealized magnetic systems. The main tool of analysis is perturbative field-theoretical renormalization group completed by resummation techniques of the perturbative series. For particular problems Monte Carlo simulations and nonperturbative renormalization group approach were used for their comprehensive study. Analyzing influence of the realistic features on the critical properties of magnets several problems were solved and a number of important results were obtained. Within study of the critical dynamics of three-dimensional magnets with different types of structural disorder the dependencies of dynamical critical exponents on the temperature distance to critical point were calculated for different initial conditions, that allows predicting scenarios of approach of real magnetic systems to asymptotic critical regime. For the first time theoretically predicted anisotropic scaling occurring in the presence of parallel extended defects in magnetic systems was confirmed by numerical simulations. For systems with such defects the enhancement of critical slowing in comparison to systems with point disorder was observed. It was shown that taking into account coupling between noncoserved order parameter and conserved quantity within model C of critical dynamics has considerable influence on dynamical critical behaviour of dicordered magnets in non-asymptotic regime. Studying the self-averaging for two-dimensional Ising model with disorder, it was shown that not all thermodynamic quantities are self-averaging in the critical region. For the Ising model with long-range correlated disorder in two dimensions mapping the problem to the theory of interaction fermions an estimate for pair correlation function critical exponent was obtained for the first time. Moreover, it was demonstrated that this model and two-dimensional Ashkin-Teller model with colors and long-range correlated disorder belong to the same universality class. The dependence of conditions of realization of different types of multicritical behaviour in an anisotropic Heisenberg antiferromagnet in an external magnetic field applied along anisotropy axis was studied within model with two coupled order parameters. Calculating the marginal dimensions of the order parameters for this model and estimating them at space dimension d=3, a conclusion, that the tetracritical behavior is realized for the considered problem in the asymptotic region, is made. Considering the problem of phase transition into noncollinear ordering for frustrated magnets, which are characterised by tensor order parameter and symmetry O(n)xO(2), nonphysical solutions, describing the critical behaviour of the field theoretical model in three dimensions for real values n=2, n=3 of the order parameter dimension, were identified. This result completed by an estimate of the marginal dimension of the order parameter obtained within nonperturbative renormalization group serves as a basis for conclusion about first order phase transition for such systems.