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

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.

Critical dynamics and effective exponents of magnets with extended impurities

“…There, the distribution of defects is characterized by the pair correlation function, falling off with distance for large separations according to a power law. The influence of such correlated defects on criticality was a subject of several theoretical studies [23,24] and predicted new universal critical behavior found recently its confirmation in the MC simulations [25].…”

“…Indeed, magnetic crystals often contain defects of a more complex structure: linear dislocations, disclinations, complexes of non-magnetic impurities, embedded in the matrix of the original crystal [14]. Theoretical studies of critical behavior of magnets containing such "extended" (macroscopic) defects have attracted considerable interest [15,16,17,18,19,20,21,22,23,24,25,26], however, a systematic experimental analysis still remains to be performed.…”

Two-dimensional quantum gravity - a laboratory for fluctuating graphs and quenched connectivity disorder

“…Such correlations for a random-bond model have been considered occasionally [70][71][72][73] and altered relevance criteria have been proposed [70,74]. Luck [74] has considered a class of irregular systems not covered by the random-bond paradigm, namely that of quasi-crystalline or aperiodic structures, and formulated a generalised relevance criterion.…”

Nonequilibrium critical relaxation in the presence of extended defects

“…15,20 The possible alternative to the isotropic scenario realized in the WH model is the anisotropic scenario realized in the model proposed by Dorogovtsev,21 in which defects are strongly correlated in ε d dimensions and randomly distributed over the remainingd = d − ε d dimensions. The case ε d = 0 is associated with uncorrelated pointlike defects, while the extended linear (planar) defects are related to the cases ε d = 1 (2).…”