Statistics of layered zigzags: a two-dimensional generalization of TASEP

TL;DR

This paper introduces a new 2+1 dimensional discrete growth model with three equivalent formulations, demonstrating its coarse-grained behavior aligns with the 2D KPZ equation and deriving its parameters from the fundamental diagram.

Contribution

It presents a novel 2+1D growth model with multiple formulations and links its hydrodynamics to the 2D KPZ equation, including a conjecture for the flow-density curve.

Findings

Model described by three equivalent formulations

Coarse-grained behavior matches 2D KPZ equation

Derived coefficients from steady state flow-density curve

Abstract

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.