On the glassy nature of random directed polymers in two dimensions

Abstract

We study numerically directed polymers in a random potential in 1 + 1 dimensions. We introduce two copies of the polymer, coupled through a thermodynamic local interaction. We show that the system is unstable versus an arbitrary weak repulsion of the two copies. This suggests a similarity with a spin glass phase, with several « valleys », where the typical differences of the free energies of the valleys grow like tω, where t is the length of the polymer and ω is probably equal to 1/3. The effect of a transverse electric field is studied in details showing the existence of strong fluctuations from sample to sample in the corresponding susceptibility. The results of the simulations are compared to analytic computations using the quantum mechanical formulation of the problem and the Bethe Ansatz.