Elastic systems with correlated disorder
Andrei A. Fedorenko
LPT-ENS
Lundi 14/01/2008, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We applied the functional renormalization group to elastic systems such as interfaces or lattices pinned by correlated quenched disorder considering two different types of correlations: columnar disorder and quenched defects correlated as $\sim x^{-a}$ for large separation $x$. We computed the critical exponents and the response to a transverse field $h$ to two-loop order. The correlated disorder violates the statistical tilt symmetry resulting in nonlinear response to a tilt. Elastic systems with columnar disorder exhibit a transverse Meissner effect: disorder generates the critical field $h_c$ below which there is no response to a tilt, and above which the tilt angle behaves as $\vartheta\sim(h-h_c)^{\phi}$ with a universal exponent $\phi < 1$. This describes the destruction of a weak Bose glass in type-II superconductors with columnar disorder caused by tilt of the magnetic field. For isotropic long-range correlated disorder the linear tilt modulus vanishes at small fields leading to a power-law response $\vartheta\sim h^{\phi}$ with $\phi > 1$. The obtained results is applied to the Kardar-Parisi-Zhang equation with temporally correlated noise. We also studied the long-distance properties of $O(N)$ spin systems with long-range correlated random fields and random anisotropies. Below the lower critical dimension, there exist two different types of quasi-long-range-order with zero order-parameter but infinite correlation length.