Joint Free-Energy Distribution in the Random Directed Polymer Problem

V. S. Dotsenko, L. B. Ioffe, V. B. Geshkenbein, S. E. Korshunov, and G. Blatter
Phys. Rev. Lett. 100, 050601 – Published 4 February 2008

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 F¯ and the free-energy difference F of the two configurations, we determine the joint distribution function PL,u(F¯,F) using the replica approach. We find that for large L and large negative free energies F¯, the joint distribution function factorizes into longitudinal [PL,u(F¯)] and transverse [Pu(F)] components, which furthermore coincide with results obtained previously via different independent routes.

  • Figure
  • Received 25 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.050601

©2008 American Physical Society

Authors & Affiliations

V. S. Dotsenko1,4, L. B. Ioffe2, V. B. Geshkenbein3,4, S. E. Korshunov4, and G. Blatter3

  • 1LPTL, Université Paris VI, 75252 Paris, France
  • 2Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 3Theoretische Physik, ETH-Zurich, 8093 Zurich, Switzerland
  • 4L.D. Landau Institute for Theoretical Physics, 119334 Moscow, Russia

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Issue

Vol. 100, Iss. 5 — 8 February 2008

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