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Temperature-induced crossovers in the static roughness of a one-dimensional interface | Elisabeth Agoritsas
; Vivien Lecomte
; Thierry Giamarchi
; | Date: |
20 Aug 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 $xi$ 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 $xi$ 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 ’critical’ 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 $B(r)sim T^{2
ext{ horn}} r^{2 zeta}$ and its corresponding exponent $ ext{ horn}$. 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. | Source: | arXiv, 1008.3570 | Services: | Forum | Review | PDF | Favorites |
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