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Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation: numerical study | | Elisabeth Agoritsas
; Vivien Lecomte
; Thierry Giamarchi
; | | Date: |
10 May 2013 | | Abstract: | We study numerically the geometrical and free-energy fluctuations of a static
one-dimensional (1D) interface with a short-range elasticity, submitted to a
quenched random-bond Gaussian disorder of finite correlation length $xi>0$,
and at finite temperature $T$. Using the exact mapping from the static 1D
interface to the 1+1 Directed Polymer (DP) growing in a continuous space, we
focus our analysis on the disorder free-energy of the DP endpoint, a quantity
which is strictly zero in absence of disorder and whose sample-to-sample
fluctuations at a fixed growing ’time’ $t$ inherit the statistical
translation-invariance of the microscopic disorder explored by the DP.
Constructing a new numerical scheme for the integration of the
Kardar-Parisi-Zhang (KPZ) evolution equation obeyed by the free-energy, we
address numerically the ’time’- and temperature-dependence of the disorder
free-energy fluctuations at fixed finite $xi$. We examine on one hand the
amplitude $ ilde{D}_{t}$ and effective correlation length $ ilde{xi}_t$ of
the free-energy fluctuations, and on the other hand the imprint of the specific
microscopic disorder correlator on the large-’time’ shape of the free-energy
two-point correlator. We observe numerically the crossover to a low-temperature
regime below a finite characteristic temperature $T_c(xi)$, as previously
predicted by Gaussian-Variational-Method (GVM) computations and scaling
arguments, and extensively investigated analytically in [Phys. Rev. E, 87
042406 (2013)]. Finally we address numerically the ’time’- and
temperature-dependence of the roughness $B(t)$, which quantifies the DP
endpoint transverse fluctuations, and we show how the amplitude
$ ilde{D}_{infty}(T,xi)$ controls the different regimes experienced by
$B(t)$ -- in agreement with the analytical predictions of a DP ’toymodel’
approach. | | Source: | arXiv, 1305.2364 | | Services: | Forum | Review | PDF | Favorites | |
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