Interfering directed paths and the sign phase transition

@article{Kim2011InterferingDP,
  title={Interfering directed paths and the sign phase transition},
  author={Hyungwon Kim and David A. Huse},
  journal={Physical Review B},
  year={2011},
  volume={83},
  pages={052405}
}
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… 
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