Interfering directed paths and the sign phase transition
Disordered Systems and Neural Networks
2011-03-15 v1 Statistical Mechanics
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 {\ss}1+1 dimensions, demonstrating the instability of the Ising ordered phase there.
Cite
@article{arxiv.1010.0053,
title = {Interfering directed paths and the sign phase transition},
author = {Hyungwon Kim and David A. Huse},
journal= {arXiv preprint arXiv:1010.0053},
year = {2011}
}
Comments
4 pages, 4 figures