Non-Gaussian effects and multifractality in the Bragg glass

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 , 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.