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- W2034315705 abstract "We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $ensuremath{phi}(x)$ subject to a Gaussian random potential $V(ensuremath{phi},x)$ and confined within a plane. We mainly concentrate on the short-scale and finite-temperature behavior of this problem described by a short but finite-ranged disorder correlator $U(ensuremath{phi})$ and introduce two types of approximations amenable to exact solutions. Expanding the disorder potential $V(ensuremath{phi},x)ensuremath{approx}{V}_{0}(x)+f(x)ensuremath{phi}(x)$ at short distances, we study the random-force (or Larkin) problem with ${V}_{0}(x)=0$ as well as the shifted random-force problem including the random offset ${V}_{0}(x)$; as such, these models remain well defined at all scales. Alternatively, we analyze the harmonic approximation to the correlator $U(ensuremath{phi})$ in a consistent manner. Using direct averaging as well as the replica technique, we derive the distribution functions ${mathcal{P}}_{L,y}(F)$ and ${mathcal{P}}_{L}(F)$ of free energies $F$ of a polymer of length $L$ for both fixed $[ensuremath{phi}(L)=y]$ and free boundary conditions on the displacement field $ensuremath{phi}(x)$ and determine the mean displacement correlators on the distance $L$. The inconsistencies encountered in the analysis of the harmonic approximation to the correlator are traced back to its nonspectral correlator; we discuss how to implement this approximation in a proper way and present a general criterion for physically admissible disorder correlators $U(ensuremath{phi})$." @default.
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- W2034315705 date "2010-11-04" @default.
- W2034315705 modified "2023-10-01" @default.
- W2034315705 title "Free-energy distribution functions for the randomly forced directed polymer" @default.
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- W2034315705 doi "https://doi.org/10.1103/physrevb.82.174201" @default.
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