Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuations

Abstract : We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the directed polymer, described by its roughness, and the fluctuations of its free-energy, characterized by its two-point correlator. Analytical arguments are provided in favor of a generic scaling law between those quantities, at finite time, non-vanishing {\xi} and explicit temperature dependence. Numerical results are in good agreement both for simulations on the discrete directed polymer and on a continuous directed polymer (with short-range correlated disorder). Applications to recent experiments on liquid crystals are discussed.
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Elisabeth Agoritsas, Sebastian Bustingorry, Vivien Lecomte, Gregory Schehr, Thierry Giamarchi. Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 86 (3), pp.031144. ⟨10.1103/PhysRevE.86.031144⟩. ⟨hal-00713432⟩

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