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arXiv:cond-mat/9907378 · Journal of Physics A Mathematical and General

Critical behaviour of 3D systems with long-range correlated quenched defects

Vladimir V. Prudnikov, Andrei A. Fedorenko

Published Aug 26, 1999• 32 citations
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Abstract

A field-theoretic description of the 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 a 3, a renormalization analysis of the scaling function 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 critical exponents in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.

DOI
10.1088/0305-4470/32/36/102

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A field-theoretic description of the 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 a 3, a renormalization analysis of the scaling function 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 critical exponents in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.
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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. PACS: 64.60.Ak; 64.60.-i; 64.60.FrIn last years, much effort has been devoted to investigation of the critical behaviour of solids containing quenched defects. In most papers considerations have been restricted to the case of point defects with small concentrations so that the defects and corresponding random fields have been assumed to be Gaussian distributed and δ- correlated. For the first time in work of Weinrib and Halperin (WH) [1] have been offered the model of the critical behaviour of disordered system in which the correlation function of the random local transition temperature g(x −y) =<< Tc(x)Tc(y)>> − << Tc(x)>> 2
A field-theory description of the static and dynamic critical behavior of systems with quenched defects obeying power law correlations $\ensuremath{\sim}|\mathbf{x}{|}^{\ensuremath{-}a}$ for large separations x\mathbf{x}x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2< a< 3,2<~a<~3,2< a< 3, 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 behavior are identified. The obtained results essentially differ from results evaluated by a double $\ensuremath{\varepsilon},\ensuremath{\delta}$ expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Pad\'e-Borel summation technique.
A eld-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 eective Hamiltonian of the model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation.For the case with rst-step RSB the xed points (FPs) corresponding to the stability of the various types of critical behaviour are identi ed with the use of the Pad e{Borel summation technique.The analysis of FPs has shown a stability of the critical behaviour of the weakly disordered three-and two-dimensional systems with respect to RSB eects and realization of the former scenario of disorder in uence on critical behaviour.For the case of systems with arbitrary dimension from 3 to 4 the ranges of critical behaviour determined by the RSB eects are found for each value of the p-component order parameter without the use of "-expansion.A comparison with the results of the "-expansion calculations is carried out.
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.
Monte Carlo simulations of the short-time dynamic behaviour are reported for three-dimensional Ising model and XY-model with long-range spatially correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are computed with the use of the corrections to scaling. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behaviour of this model in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.