J. Phys. I France
Volume 2, Numéro 8, August 1992
Page(s) 1607 - 1619
DOI: 10.1051/jp1:1992230
J. Phys. I France 2 (1992) 1607-1619

Directed walks with complex random weights: phase diagram and replica symmetry breaking

Yadin Y. Goldschmidt and Thomas Blum

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

(Received 26 February 1992, accepted in final form 21 April 1992)

We consider the problem of directed walks (or polymers) in a random potential with both real and imaginary parts. The correlations of the potential are of short range. The problem is solved using a variational approximation which is expected to become exact in the limit of a large embedding dimension. A rich phase diagram is found which contains five phases. In addition to the simple high temperature phase, there are four ordered phases with different degrees of replica-symmetry-breaking. Three of the phases are dominated by interference (quantum) effects, and in two phases a pairing interaction between replicas plays an important role.

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