Commensurate-Incommensurate Transitions of the 1D Disordered Chiral Clock Model

TL;DR

This paper investigates how quenched disorder affects phase transitions in the 1D $ ext{Z}_N$ chiral clock model, revealing a rounding mechanism that alters the nature of the transition.

Contribution

It introduces a detailed analysis of disorder effects on commensurate-incommensurate transitions using density-matrix renormalization group methods.

Findings

Disorder rounds sharp phase transitions in the model.

Domain wall density shows an essential singularity.

Order parameter exhibits a discontinuity at the transition.

Abstract

We study the effects of quenched disorder on the commensurate-incommensurate transitions in the 1D $\mathbb{Z}_N$ chiral clock model. The interplay of domain walls and rare regions rounds the sharp transitions of the pure model. The density of domain walls displays an essential singularity, while the order parameter develops a discontinuity at the transition. We perform extensive density-matrix renormalization group calculations to support theoretical predictions. Our results provide a distinct rounding mechanism of continuous phase transitions in disordered systems.