On the scaling properties of (2+1) directed polymers in the high temperature limit

Abstract

In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $\theta =1/2$ which is different from the zero-temperature numerical value which is close to 0.241. This result implies that unlike the $(1+1)$ system in the two-dimensional case the free energy scaling exponent is non-universal being temperature dependent.

arXiv comment9 pages, 3 figures

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