| Numéro |
J. Phys. I France
Volume 3, Numéro 11, November 1993
|
|
|---|---|---|
| Page(s) | 2179 - 2198 | |
| DOI | https://doi.org/10.1051/jp1:1993240 | |
J. Phys. I France 3 (1993) 2179-2198
Directed polymers in the presence of columnar disorder
Joachim Krug1 and Timothy Halpin-Healy21 Institut für Festkörperforschung, Forschungszentrum Jülich, P.O. Box 1913, D-52425 Jülich, Germany
2 Physics Departement, Barnard College, Columbia University, New York, NY 10027-6598, U.S.A.
(Received 10 March 1993, revised 28 June 1993, accepted 21 July 1993)
Abstract
We consider directed polymers in a random landscape that is completely correlated in the time direction. This problem is closely
related to diffusion-reproduction processes and undirected Gaussian polymers in a disordered environment. In contrast to the
case of uncorrelated disorder, we find the behavior to be very different at zero temperature, where the scaling exponents
depend on the details of the random energy distribution, and at finite temperature, where the transverse wandering is subballistic,
with
for bounded distributions in
d + 1 dimensions. Numerically, these strong logarithmic corrections give rise to apparently nontrivial effective exponents. Our
analytic results are based on appropriate Flory expressions for the (free) energy at
T = 0 and
T > 0. Some universal statistical properties of the evolutionary hopping of the optimal path are also derived.
© Les Editions de Physique 1993