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arXiv:cond-mat/0412040 · Physical Review B

Nonequilibrium critical relaxation in the presence of extended defects

Andrei A. Fedorenko

Published Apr 2, 2004• 15 citations
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Abstract

We study nonequilibrium critical relaxation properties of systems with quenched extended defects, correlated in ${\ensuremath{\varepsilon}}_{d}$ dimensions and randomly distributed in the remaining $d\ensuremath{-}{\ensuremath{\varepsilon}}_{d}$ dimensions. Using a field-theoretic renormalization-group approach, we find the scaling behavior of the nonequilibrium response and correlation functions and calculate the initial slip exponents $\ensuremath{\theta}$ and ${\ensuremath{\theta}}^{\ensuremath{'}},$ which describe the growth of correlations during the initial stage of the critical relaxation, in the two-loop approximation.

DOI
10.1103/physrevb.69.134301

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We investigate the critical properties of d-dimensional magnetic systems with quenched extended defects, correlated in ${\ensuremath{\varepsilon}}_{d}$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d\ensuremath{-}{\ensuremath{\varepsilon}}_{d}$ dimensions; both in the case of fixed dimension d=3d=3d=3 and when the space dimension continuously changes from the lower critical dimension to the upper one. Our renormalization-group calculations are performed in the minimal subtraction scheme. We analyze the two-loop renormalization-group functions for different fixed values of the parameters $d,{\ensuremath{\varepsilon}}_{d}.$ To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the universality class of this system.
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.
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Static and dynamic critical behaviour is studied for spin systems with quenched impurities that are correlated along an epsilon d -dimensional 'line' and randomly distributed in d- epsilon d dimensions. These impurities make the system anisotropic and modify its critical properties. Critical exponents are calculated at the second order of an expansion in epsilon and epsilon d (with epsilon =4-d). Although renormalisation-group functions depend on the ratio epsilon d /( epsilon + epsilon d ), critical exponents are found not to involve this ratio. Pade-like approximants are used to give numerical estimates for the exponents.