A. A. Fedorenko

Static and dynamic critical properties of 3D systems with long-range correlated quenched defects

A field-theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations ~|x|-a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double ,-expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

Stability of critical behavior of weakly disordered systems with respect to the replica symmetry breaking

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For case with 1-step RSB the fixed points (FPs) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FPs has shown a stability of the critical behaviour of the weakly disordered systems with respect to RSB effects and realization of former scenario of disorder influence on critical behaviour.

Stability of critical behaviour of weakly disordered systems to introduction of potentials with replica symmetry breaking

A field-theoretic description of the critical behaviour of the weakly disordered systems with p-component order parameter is given. Directly, for three-dimensional systems a renormalization analysis of the effective replicated Hamiltonian of a model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For the case with first-step RSB the fixed points (FPs) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FPs has shown a stability of the critical behaviour of the weakly disordered systems with respect to RSB effects and realization of the former scenario of disorder influence on critical behaviour.

Field-theoretic description of the multicritical behavior of systems with two order parameters

A field-theoretic description of phase transformations in complex systems with two interacting order parameters is given. For three-dimensional systems in the two-loop approximation a renormalization-group analysis of the scaling functions is carried out directly, and the fixed points corresponding to stability of the bicritical and tetracritical behavior are identified. The critical exponents at the multicritical points in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.

Multicritical behavior of weakly disordered systems with two order parameters

We present a field-theoretic description of phase transitions in weakly disordered systems with two coupled order parameters. Using the two-loop approximation and the Padé-Borel summation technique, we carry out a renormalization-group analysis of the scaling functions for three-dimensional systems and identify the fixed points corresponding to stable multicritical behavior. We also study the effect of frozen point impurities on the nature of the phase diagrams.

Stability of the critical behavior of weakly disordered systems with respect to the introduction of an interaction potential breaking replica symmetry

The critical behavior of weakly disordered systems with a p-component order parameter is described using field-theoretic methods. A renormalization-group analysis of the effective model replica Hamiltonian with an interaction potential breaking replica symmetry is performed directly for three-dimensional systems in the two-loop approximation. For the case of a one-step replica symmetry breaking, fixed points of renormalization group equations are found using the Padé-Borel summation technique. It is established that the critical behavior of weakly disordered systems is stable with respect to replica symmetry breaking and that the former scenario of the influence of structural defects on the critical behavior of these systems is realized.

Stability of the critical behavior of weakly disordered systems against replica symmetry breaking

A field-theoretical approach is used to describe the critical behavior of weakly disordered systems with a p-component order parameter. Renormalization group (RG) analysis of the effective replica Hamiltonian of a model with replica-unsymmetrical interaction potential is carried out in a two-loop approximation directly for three-dimensional systems. The Padé-Borel summation technique is used to determine fixed points of the RG equations for the case of a single-step replica symmetry breaking (RSB). Analysis of their stability showed that the type of stable critical behavior of the disordered systems against the RSB effects remains as before.