Joint free-energy distribution in the random directed polymer problem.
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[over ] and the free-energy difference F;{'} of the two configurations, we determine the joint distribution function P(L,u)(F[over ],F(')) using the replica approach. We find that for large L and large negative free energies F[over ], the joint distribution function factorizes into longitudinal [P(L,u)(F[over ])] and transverse [P(u)(F('))] components, which furthermore coincide with results obtained previously via different independent routes.
Dotsenko
V S
VS
LPTL, Université Paris VI, 75252 Paris, France.
Ioffe
L B
LB
Geshkenbein
V B
VB
Korshunov
S E
SE
Blatter
G
G