Non-Gaussian effects and multifractality in the Bragg glass

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 - epsilon, the even n-th cumulant of relative displacements as [GRAPHICS] similar or equal to A(n) ln r with A(n) = -(epsilon/3)(n)Gamma(n - 1/2)zeta(2n - 3)/root pi, as well as the multifractal dimension xq of the exponential field e(qu(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. Copyright (C) EPLA, 2014