Anomalous fluctuations of directed polymers in random media
Abstract
A systematic analysis of largescale fluctuations in the lowtemperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states.'' The probability distribution of their sizes is found to have a powerlaw tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with ``broken replica symmetry.'' It is argued that the powerlaw distribution of large thermally active excitations is a consequence of the continuous statistical ``tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.
 Publication:

Physical Review B
 Pub Date:
 February 1994
 DOI:
 10.1103/PhysRevB.49.3136
 arXiv:
 arXiv:condmat/9309016
 Bibcode:
 1994PhRvB..49.3136H
 Keywords:

 05.50.+q;
 75.10.Nr;
 74.60.Ge;
 Lattice theory and statistics;
 Spinglass and other random models;
 Condensed Matter
 EPrint:
 59 pages including 8 figures ( REVTEX 3.0 )Email: hwa@cmt.harvard.edu