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A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations ∼ |x| −a for large separations x is given. Directly for three-dimensional systems and different values of correlation parameter 2 ≤ a ≤ 3 a renormalization analysis of scaling function in the two-loop approximation is carried out, and the fixed points corresponding to stability of the various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by double ε, δ -expansion. The critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

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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 (FP's) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FP's 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.

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Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ ′ of the short time evolution of a system with an n-component order parameter is calculated within a dynamical dissipative model using the method of ε-expansion in a threeloop approximation. Numerical values of θ ′ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.