Joint FreeEnergy Distribution in the Random Directed Polymer Problem
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 freeenergy F¯ and the freeenergy difference F^{'} of the two configurations, we determine the joint distribution function P_{L,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 [P_{L,u}(F¯)] and transverse [P_{u}(F^{'})] components, which furthermore coincide with results obtained previously via different independent routes.
 Publication:

Physical Review Letters
 Pub Date:
 February 2008
 DOI:
 10.1103/PhysRevLett.100.050601
 arXiv:
 arXiv:0705.0220
 Bibcode:
 2008PhRvL.100e0601D
 Keywords:

 05.20.y;
 61.41.+e;
 74.25.Qt;
 75.10.Nr;
 Classical statistical mechanics;
 Polymers elastomers and plastics;
 Vortex lattices flux pinning flux creep;
 Spinglass and other random models;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 4 pages, 1 figure