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

2007/12/31 by Andrei A. Fedorenko
Mathematics · Physics and Astronomy · #Condensed matter physics #Exponent #Geometry #Isotropy #Mathematical physics #Mathematics #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #Tilt (camera) #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.77.094203

published as Phys. Rev. B 77, 094203 (2008) · 15 pages, 8 figures, revtex4

openalex publication_date 2008/03/14 · arxiv created 2008/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 \ensuremath∼x^\ensuremath-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 \ensuremathϑ\ensuremath∼(h\ensuremath-h_c)^\ensuremathφ with a universal exponent \ensuremathφ<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 \ensuremathϑ\ensuremath∼h^\ensuremathφ with \ensuremathφ>1. The obtained results are applied to the Kardar-Parisi-Zhang equation with temporally correlated noise.

Citations

• Depinning transition at the upper critical dimension
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