  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
<[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(\epsilon/3)^n \Gamma(n-1/2)
\zeta(2n-3)/\pi^(1/2), as well as the multifractal dimension x_q of the
exponential field e^{q 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.
