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 ξ 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 ξ 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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Cited by in corpus (4)

• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interface
• Zero temperature limit for (1+1) directed polymers with correlated random potential
• Microscopic interplay of temperature and disorder of a one-dimensional elastic interface