Non-Gaussian effects and multifractality in the Bragg glass
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
Received: 27 September 2013
Accepted: 21 December 2013
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 , the even n-th cumulant of relative displacements as with , as well as the multifractal dimension xq of the exponential field . 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.
PACS: 68.35.Rh – Phase transitions and critical phenomena / 11.25.Tq – Gauge/string duality
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