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arXiv · 1206.6592

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

Elisabeth Agoritsas·Sebastian Bustingorry·Vivien Lecomte·Gregory Schehr·Thierry Giamarchi
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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. 2012-06-28. Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuations. https://doi.org/10.1103/physreve.86.031144

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