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

Elisabeth Agoritsas 1, * Sebastian Bustingorry 2 Vivien Lecomte 3 Gregory Schehr 4 Thierry Giamarchi 1

Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 86 (3), pp.031144. <10.1103/PhysRevE.86.031144>

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.

  • 1. DPMC - Département de Physique de la Matière Condensée
  • 2. Centro Atomico Bariloche
  • 3. LPMA - Laboratoire de Probabilités et Modèles Aléatoires
  • 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques