Interfering directed paths and the sign phase transition

Abstract

We revisit the question of the "sign phase transition" for interfering directed paths with real amplitudes in a random medium. The sign of the total amplitude of the paths to a given point may be viewed as an Ising order parameter, so we suggest that a coarse-grained theory for system is a dynamic Ising model coupled to a Kardar-Parisi-Zhang (KPZ) model. It appears that when the KPZ model is in its strong-coupling ("pinned") phase, the Ising model does not have a stable ferromagnetic phase, so there is no sign phase transition. We investigate this numerically for the case of ß1+1 dimensions, demonstrating the instability of the Ising ordered phase there.

4 pages, 4 figures

References in corpus (2)

• Phase ordering and roughening on growing films
• Directed paths on hierarchical lattices with random sign weights

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