The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius

Details The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius

1997-09-24

arxiv.org/abs/cond-mat/9709258v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, Latex

Scientific paper

10.1088/0305-4470/31/11/009

We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a directed polymer with delta-correlated random potential can be applied for the description of the present system only in the high-temperature limit. For the low temperature limit we have obtained the new solution which is described by the one-step replica symmetry breaking. For the mean square deviation of the directed polymer of the linear size L it provides the usual scaling $L^{2z}$ with the wandering exponent z = 2/3 and the temperature-independent prefactor.

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