Elastic systems with correlated disorder: Response to tilt and application to surface growth

TL;DR

This paper investigates the response of elastic systems with correlated disorder to tilt, revealing nonlinear behaviors and phase transitions, with applications to surface growth and superconductors.

Contribution

It provides a two-loop order analysis of critical exponents and response functions for elastic systems with correlated disorder, including novel effects like the transverse Meissner effect.

Findings

Disorder induces a critical field h_c for the transverse Meissner effect.

Elastic systems with long-range correlated disorder show power-law tilt responses.

Results apply to the KPZ equation with temporally correlated noise.

Abstract

We study elastic systems such as interfaces or lattices pinned by correlated quenched disorder considering two different types of correlations: generalized columnar disorder and quenched defects correlated as ~ x^{-a} for large separation x. Using functional renormalization group methods, we obtain the critical exponents to two-loop order and calculate the response to a transverse field h. 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 \theta ~ (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 \theta ~ h^{\phi} with \phi>1. The obtained results are applied to the Kardar-Parisi-Zhang equation with temporally correlated noise.