Universal properties of the Kardar-Parisi-Zhang equation with quenched columnar disorders

TL;DR

This paper investigates the universal scaling behavior of the KPZ equation with quenched columnar disorder across dimensions, revealing propagating modes that influence universality classes and identifying a new transition at the critical dimension d=4.

Contribution

It demonstrates that propagating modes caused by quenched disorder render the disorder effects irrelevant, preserving KPZ universality, and uncovers a new universality class at the critical dimension d=4.

Findings

Propagating modes induce anisotropy in the system.

Disorder effects become irrelevant due to propagating modes.

A new universality class emerges at dimension d=4.

Abstract

Inspired by the recent results on totally asymmetric simple exclusion processes on a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal scaling properties of the Kardar-Parisi-Zhang (KPZ) equation with short-ranged quenched columnar disorder in general d-dimensions. We show that there are generic propagating modes in the system that have their origin in the quenched disorder and make the system anisotropic. We argue that the presence of the propagating modes actually make the effects of the quenched disorder irrelevant, making the universal long wavelength scaling property belong to the well-known KPZ universality class. On the other hand, when these waves vanish in a special limit of the model, new universality class emerges with dimension d = 4 as the lower critical dimension, above which the system is speculated to admit a disorder-induced roughening transition to a perturbatively inaccessible rough phase.