Elisabeth Agoritsas, Vivien Lecomte, Thierry Giamarchi
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 \textit{finite} correlation length $\xi$. Centering our study on the two-point correlator of the derivative of the disorder free-energy $\bar{R}(t,y)$ 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 $\bar{R}(t,y) \approx \widetilde{D}_t \cdot \mathcal{R}(y)$, 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.
View original:
http://arxiv.org/abs/1209.0567
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