Elastic systems with correlated disorder

Andrei A. Fedorenko

LPT-ENS

Mon, Jan. 14th 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.