Non-Gaussian effects and multifractality in the Bragg glass

Andrei A. Fedorenko (1) , Pierre Le Doussal (1) , Kay Joerg Wiese (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Physique [physics]; Astrophysique [astro-ph]; Matière Condensée [cond-mat]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Andrei A. Fedorenko, Pierre Le Doussal, Kay Joerg Wiese. Non-Gaussian effects and multifractality in the Bragg glass. EPL - Europhysics Letters, 2014, 105 (1), pp.16002. ⟨10.1209/0295-5075/105/16002⟩. ⟨hal-02281092⟩