J. Phys. France 51, 1595-1606 (1990)
DOI: 10.1051/jphys:0199000510150159500

On the replica approach to random directed polymers in two dimensions

Giorgio Parisi

Dipartimento di Fisica, INFN sezione Tor Vergata, Università di Roma Tor Vergata, Prolungamento di Via del Fontanile di Carcaricola, Roma 00173, Italy

Abstract
In this note we study directed polymers in a two dimensional random medium with short range noise using the replica approach. We find the predictions of the replica symmetric theory and we compare them with exact results. We consider the possibility of spontaneous symmetry breaking and we suggest that replica symmetry is weakly broken also in this two dimensional model.

PACS
0550 - Lattice theory and statistics (Ising, Potts, etc.).
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.

Key words
lattice theory and statistics -- polymers -- random processes -- spontaneous symmetry breaking