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Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation | | Elisabeth Agoritsas
; Vivien Lecomte
; Thierry Giamarchi
; | | Date: |
4 Sep 2012 | | Abstract: | Experimental realizations of a 1D interface always exhibit a finite
microscopic width $xi>0$; its existence is erased by thermal fluctuations at
sufficiently high temperatures, but turns out to be a crucial ingredient for
the description of the interface fluctuations below a characteristic
temperature $T_c(xi)$. Exploiting the exact mapping between the static 1D
interface and a 1+1 Directed Polymer (DP) growing in a continuous space, we
have studied analytically and numerically both the geometrical and the
free-energy fluctuations of a DP at finite temperature $T$, with a short-range
elasticity and submitted to a quenched random-bond Gaussian disorder of
extit{finite} correlation length $xi$.
Centering our study on the two-point correlator of the derivative of the
disorder free-energy $ar{R}(t,y)$ as a function of growing ’time’ $t$, we
explore several analytical arguments at finite $xi$ and propose a ’toymodel’
in order to characterize the temperature-dependence of the DP endpoint
fluctuations. Approximating the full correlator at small endpoint position $y$
by $ar{R}(t,y) approx widetilde{D}_t cdot mathcal{R}(y)$, we show on one
hand that the amplitude $widetilde{D}_infty (T,xi)$ correctly describes the
low- and high-temperature regimes along with the full crossover around
$T_c(xi)$. On the other hand, we discuss the close connection between the
temperature-dependent function $mathcal{R}(y)$ at asymptotically large ’times’
and the quenched disorder correlator.
Finally we discuss the consequences of the low-temperature regime for two
experimental realizations of KPZ interfaces, namely the static and quasistatic
behavior of magnetic domain walls and the high-velocity steady-state dynamics
of interfaces in liquid crystals. | | Source: | arXiv, 1209.0567 | | Services: | Forum | Review | PDF | Favorites | |
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