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arXiv · 0705.0220

Joint free energy distribution in the random directed polymer problem

V. S. Dotsenko·L. B. Ioffe·V. B. Geshkenbein·S. E. Korshunov·G. Blatter
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Abstract

We consider two configurations of a random directed polymer of length L confined to a plane and ending in two points separated by 2u. Defining the mean free energy $\bar F$ and the free energy difference F' of the two configurations, we determine the joint distribution function P_{L,u}(\bar F,F') using the replica approach. We find that for large L and large negative free energies $\bar F$, the joint distribution function factorizes into longitudinal (P_{L,u} (\bar F)) and transverse (P_{u}(F')) components, which furthermore coincide with results obtained prevously via different independent routes.

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V. S. Dotsenko, L. B. Ioffe, V. B. Geshkenbein, S. E. Korshunov, G. Blatter. 2008-01-18. Joint free energy distribution in the random directed polymer problem. https://doi.org/10.1103/physrevlett.100.050601

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