Nonequilibrium critical relaxation in the presence of extended defects

We study the long-distance behavior of the O(N ) model in the presence of random fields and random anisotropies correlated as ∼ 1/x d−σ for large separation x using the functional renormalization group. We compute the fixed points and analyze their regions of stability within a double ε = d − 4 and σ expansion. We find that the long-range disorder correlator remains analytic but generates short-range disorder whose correlator develops the usual cusp. This allows us to obtain the phase diagrams in (d, σ, N ) parameter space and compute the critical exponents to first order in ε and σ. We show that the standard renormalization group methods with a finite number of couplings used in previous studies of systems with long-range correlated random fields fail to capture all critical properties. We argue that our results may be relevant to the behavior of 3 He-A in aerogel.

show abstract

“…The exponents describing the correlation functions in the LR QLRO phase are given by Eqs. (29) and (30). Note that below d lc we have η > 0.…”

Section: Long-range Random Anisotropy O(n ) Modelmentioning

confidence: 95%

Long-range correlated random field and random anisotropyO(N)models: A functional renormalization group study

Fedorenko

Kühnel

2007

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…The defects are d -dimensional objects ͑hyperplanes͒ extending throughout the whole system along the coordinate x ʈ and randomly distributed in the transverse directions x Ќ with the concentration taken to be well below the percolation limit. [36][37][38] The corresponding correlator of the disorder potential can be written as…”

Section: A Generalized Columnar Disordermentioning

confidence: 99%

Elastic systems with correlated disorder: Response to tilt and application to surface growth

Fedorenko

2008

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

We study elastic systems such as interfaces or lattices pinned by correlated quenched disorder considering two different types of correlations: generalized columnar disorder and quenched defects correlated as ϳx −a for large separation x. Using functional renormalization group methods, we obtain the critical exponents to twoloop order and calculate the response to a transverse field h. The correlated disorder violates the statistical tilt symmetry resulting in nonlinear response to a tilt. Elastic systems with columnar disorder exhibit a transverse Meissner effect: disorder generates the critical field h c below which there is no response to a tilt and above which the tilt angle behaves as ϳ͑h − h c ͒ with a universal exponent Ͻ 1. This describes the destruction of a weak Bose glass in type-II superconductors with columnar disorder caused by tilt of the magnetic field. For isotropic long-range correlated disorder, the linear tilt modulus vanishes at small fields leading to a power-law response ϳ h with Ͼ 1. The obtained results are applied to the Kardar-Parisi-Zhang equation with temporally correlated noise.

show abstract

“…Similarly as in the former subsection 4.2.1 we give in the table 5 the values of the observables that are used in the FSS analysis. Now one can extract the correlation length critical exponent ν from the FSS of maxima of four different quantities: temperature derivatives of logarithm of magnetization and of its square D M , D M 2 (12) and of magnetic cumulants D U 4 , D U 2 (10). Corresponding plots are given in fig.…”

Section: Averaging Bmentioning

confidence: 99%

On the universality class of the 3d Ising model with long-range-correlated disorder

Ivaneyko

Berche²,

Holovatch

et al. 2008

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of extended Harris criterion (A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413) and indicate the existence of a new universality class, the numerical values of the critical exponents found so far differ essentially. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising model with non-magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice. The Swendsen-Wang algorithm is used alongside with a histogram reweighting technique and the finite-size scaling analysis to evaluate the values of critical exponents governing the magnetic phase transition. Our estimates for these exponents differ from both previous numerical simulations and are in favour of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlations decay.

show abstract

Nonequilibrium critical relaxation in the presence of extended defects

Cited by 14 publications

References 48 publications

Long-range correlated random field and random anisotropyO(N)models: A functional renormalization group study

Long-range correlated random field and random anisotropyO(N)models: A functional renormalization group study

Elastic systems with correlated disorder: Response to tilt and application to surface growth

On the universality class of the 3d Ising model with long-range-correlated disorder

Contact Info

Product

Resources

About