Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

CRITICAL BEHAVIOUR OF 3D SYSTEMS WITH LONG-RANGE CORRELATED QUENCHED DEFECTS

V. V. Prudnikov, Andrei A. Fedorenko

Published Jan 1, 1999• 20 citations
OpenAlex

Abstract

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

Related papers

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

Vladimir V. Prudnikov, Andrei A. Fedorenko

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.

arXiv:cond-mat/9907378•Journal of Physics A Mathematical and General•Aug 26, 1999•32 citations

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

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

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.

Journal of Physics A Mathematical and General•Nov 30, 1999•32 citations

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

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

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.

Physical review. B, Condensed matter•Oct 1, 2000•76 citations

Critical Behaviour of Systems with Long-Range Correlated Quenched Defects

A. L. Korzhenevskii, A. A. Luzhkov, Hans-O Heuer

The critical behaviour of the generalized (anisotropic) m -component Weinrib-Halperin model is investigated. The critical exponent η and the dynamic exponent z are calculated in d = 4 - ε space dimension in a two- and one-loop approximation, respectively. Using the fermionic formulation we have derived an exact result for the correlation length exponent ν of the two-dimensional Ising model with long-range correlated quenched defects.

Europhysics Letters (EPL)•Oct 1, 1995•11 citations

Critical behaviour of weakly disordered systems with replica symmetry breaking potentials

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

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.

Journal of Physical Studies•Jan 1, 2001•0 citations

Critical exponent ν of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

Stanislav Kazmin, Wolfhard Janke E

We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power law ${r}^{\ensuremath{-}a}$. We derive the critical exponent of the correlation length $\ensuremath{\nu}$ and the confluent correction exponent $\ensuremath{\omega}$ in dependence of $a$ by combining different concentrations of defects $0.05\ensuremath{\le}{p}_{d}\ensuremath{\le}0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5\ensuremath{\le}a\ensuremath{\le}3.5$ as well as the uncorrelated case $a=\ensuremath{\infty}$ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent $a$ and the concentration of defects ${p}_{d}$. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $\ensuremath{\nu}=2/a$, and discuss the occurring deviations.

arXiv:2008.03169•Physical review. B./Physical review. B•Nov 20, 2020•6 citations
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-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 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-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.
We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power law ${r}^{\ensuremath{-}a}$. We derive the critical exponent of the correlation length $\ensuremath{\nu}$ and the confluent correction exponent $\ensuremath{\omega}$ in dependence of aaa by combining different concentrations of defects $0.05\ensuremath{\le}{p}_{d}\ensuremath{\le}0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5\ensuremath{\le}a\ensuremath{\le}3.5$ as well as the uncorrelated case $a=\ensuremath{\infty}$ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent aaa and the concentration of defects pd{p}_{d}pd​. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $\ensuremath{\nu}=2/a$, and discuss the occurring deviations.