M. Dudka

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.

WEAK QUENCHED DISORDER AND CRITICALITY: RESUMMATION OF ASYMPTOTIC(?) SERIES

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.

Critical dynamics and effective exponents of magnets with extended impurities

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in

Model C critical dynamics of random anisotropy magnets

\epsilon_d

Critical dynamics of diluted relaxational models coupled to a conserved density.

dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining

Universality classes of the three-dimensional mn-vector model

d-\epsilon_d

Phase Transition in the Random Anisotropy Model

dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets, the structural disorder is present in the form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However the structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching the asymptotic regime.

Model C critical dynamics of disordered magnets

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a nonconserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics; however, it is the effective critical behavior that is often observed in experiments and in computer simulations, and this is described by the full set of dynamical equations of diluted model C. Indeed, different scenarios of effective critical behavior are predicted.

Crossover between diffusion-limited and reaction-limited regimes in the coagulation–diffusion process

We study the conditions under which the critical behaviour of the three-dimensional mn-vector model does not belong to the spherically symmetrical universality class. In the calculations, we rely on the field-theoretical re- normalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions. We address the question why the renormalization-group perturbation theory expansions available for the model with a record (six loop) accuracy have not allowed so far for a definite answer about the universality class for certain particular values of dimensions m, n. We show that an analysis based on the marginal dimensions rather than on the stability exponents leads to the robust results about the phase diagram of the model.