Interfering directed paths and the sign phase transition

TL;DR

This paper investigates the sign phase transition in interfering directed paths within a random medium, proposing a coupled Ising-KPZ model and demonstrating the absence of a stable ferromagnetic phase in 1+1 dimensions.

Contribution

It introduces a coupled Ising-KPZ model to analyze the sign phase transition and provides numerical evidence of the instability of the Ising ordered phase in 1+1 dimensions.

Findings

No stable ferromagnetic phase in the strong-coupling KPZ regime.

Numerical evidence of Ising phase instability in 1+1 dimensions.

Coupled model offers new insights into sign phase transition behavior.

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.