Incommensurate Phase on a Disordered Surface: Instability Against the Formation of Overhangs and Finite Loops

TL;DR

This paper investigates the stability of the incommensurate phase in disordered two-dimensional systems, revealing an instability caused by the formation of overhangs and loops, which leads to long-range correlations and a massless boson.

Contribution

It introduces a model analyzing the instability of the incommensurate phase due to overhangs and loops, highlighting the role of replica symmetry and long-range correlations.

Findings

Probability of overhangs/loops vanishes as √ε in pure limit

Long-range correlated fluctuations in quenched system

Creation of a massless boson indicating instability

Abstract

The stability of the quenched incommensurate phase in two dimensions against the creation of overhangs and finite loops (OH/FL) in the replica space is investigated for a model of domain walls with $N$ colors. Introducing a chemical potential $\epsilon$ for OH/FL, the probability for the formation of these objects is studied for $\epsilon\to0$. In the pure limit this probability vanishes with $\sqrt{\epsilon}$, whereas the fluctuations of this probability are long-range correlated in the quenched system. This indicates an instability related to the symmetry in replica space. It is accompanied by the creation of a massless boson. The latter leads to a power law decay with exponent $\propto 1/N$ for the product of the correlation functions along the domain walls.