Interfering directed paths and the sign phase transition

Hyungwon Kim, David A. Huse

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 this 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 1+1 dimensions, demonstrating the instability of the Ising ordered phase there.

Original languageEnglish (US)
Article number052405
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number5
StatePublished - Feb 24 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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