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Physical review. B, Condensed matter

Field-theory approach to critical behavior of systems with long-range correlated defects

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Andrei A. Fedorenko

Published Oct 1, 2000• 76 citations
Publisher

Abstract

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 $\mathbf{x}$ is given. Directly, for three-dimensional systems and for different values of the correlation parameter, $2<~a<~3,$ a renormalization analysis of the scaling 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.

DOI
10.1103/physrevb.62.8777

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A field-theory description of the static and dynamic critical behavior of systems with quenched defects obeying power law correlations \ensuremath∼∣x∣\ensuremath−a\ensuremath{\sim}|\mathbf{x}{|}^{\ensuremath{-}a}\ensuremath∼∣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 \ensuremathε,\ensuremathδ\ensuremath{\varepsilon},\ensuremath{\delta}\ensuremathε,\ensuremathδ 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 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 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 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 Padé-Borel summation technique.
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.
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
We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)(d=3)(d=3)-dimensional magnets with quenched extended defects, correlated in ${\ensuremath{\epsilon}}_{d}$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d\ensuremath{-}{\ensuremath{\epsilon}}_{d}$ 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 AAA dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding nonuniversal exponents.
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.
The simultaneous effect of nonequilibrium initial states and correlation between defects of the structure on the evolution of anisotropic disordered systems at the critical point has been analyzed. The field theory description of the nonequilibrium critical behavior of three-dimensional disordered systems with the longrange correlated defects has been given and the dynamical critical exponent of the short-time evolution has been calculated in the two-loop approximation without the use of the ɛ expansion. The values of the dynamical critical exponent obtained by using various methods for summing asymptotic series have been compared with the results of the computer simulation of the nonequilibrium critical behavior of the three-dimensional disordered Ising model in the short-time regime.