Non-Gaussian effects and multifractality in the Bragg glass

Andrei A. Fedorenko; Pierre Le Doussal; Kay Joerg Wiese

doi:10.1209/0295-5075/105/16002

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arXiv · 1309.6529

Non-Gaussian effects and multifractality in the Bragg glass

Andrei A. Fedorenko·Pierre Le Doussal·Kay Joerg Wiese

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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-epsilon, the even n-th cumulant of relative displacements as <[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(ε/3)^n Γ(n-1/2) ζ(2n-3)/π^(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.

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Andrei A. Fedorenko, Pierre Le Doussal, Kay Joerg Wiese. 2013-09-25. Non-Gaussian effects and multifractality in the Bragg glass. https://doi.org/10.1209/0295-5075%2F105%2F16002

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