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Temperature-induced crossovers in the static roughness of a one-dimensional interface

Elisabeth Agoritsas, Vivien Lecomte, and Thierry Giamarchi
Phys. Rev. B 82, 184207 – Published 22 November 2010

Abstract

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian variational method (GVM), we explore the consequences of a finite interface width ξ on the small-lengthscale fluctuations. We compute analytically the static roughness B(r) of the interface as a function of the distance r between two points on the interface. We focus on the case of short-range elasticity and random-bond disorder. We show that for a finite width ξ two temperature regimes exist. At low temperature, the expected thermal and random-manifold regimes, respectively, for small and large scales, connect via an intermediate “modified” Larkin regime, that we determine. This regime ends at a temperature-independent characteristic “Larkin” length. Above a certain characteristic temperature that we identify, this intermediate regime disappears. The thermal and random-manifold regimes connect at a single crossover lengthscale, that we compute. This is also the expected behavior for zero width. Using a directed polymer description, we also study via a second GVM procedure and generic scaling arguments, a modified toy model that provides further insights on this crossover. We discuss the relevance of the two GVM procedures for the roughness at large lengthscale in those regimes. In particular, we analyze the scaling of the temperature-dependent prefactor in the roughness B(r)T2þr2ζ and its corresponding thorn exponent þ. We briefly discuss the consequences of those results for the quasistatic creep law of a driven interface, in connection with previous experimental and numerical studies.

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  • Received 20 August 2010

DOI:https://doi.org/10.1103/PhysRevB.82.184207

©2010 American Physical Society

Authors & Affiliations

Elisabeth Agoritsas1,*, Vivien Lecomte1,2, and Thierry Giamarchi1

  • 1DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
  • 2Laboratoire de Probabilités et Modèles Aléatoires (CNRS UMR 7599), Université Paris Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France

  • *elisabeth.agoritsas@unige.ch

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Vol. 82, Iss. 18 — 1 November 2010

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