Non-Gaussian effects and multifractality in the Bragg glass
Andrei A. Fedorenko1, Pierre Le Doussal2, Kay Jörg Wiese2
1 CNRS-Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, 69007 Lyon, France.
2
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France.
Abstract
We study, beyond the Gaussian approximation, the
decay of the translational order correlation function for a d-dimensional
scalar periodic elastic system in a disordered environment.
We develop a method based on functional determinants,
equivalent to summing an infinite set of diagrams. We obtain, in dimension d = 4 − ε, the
even n-th cumulant of relative displacements as ⟨[u(r) − u(0)]n⟩c
≃ An ln r with An = − (ε/3)n Γ(n − ½) ζ(2n − 3)/π½, as well as the multifractal dimension xq of the exponential field eq u(r). As a corollary, we obtain an analytic expression for a class of n-loop integrals in d = 4, which appear in the perturbative determination of Konishi amplitudes, also accessible via AdS/CFT using integrability.
arXiv:1309.6529 [pdf]
EPL 105 (2014) 16002 [pdf]
Copyright (C) by Kay Wiese. Last edited January 31, 2014.