Incommensurate phase on a disordered surface: Instability against the formation of overhangs and finite loops

The stability of the quenched incommensurate phase in two dimensions against the creation of overhangs (OHs) and finite loops (FLs) in the fermion replica space is investigated for a model of domain walls with N colors. Introducing a chemical potential ε for OHs and FLs, the probability for the formation of these objects is studied for ε→0. In the pure limit this probability vanishes with ε, whereas the fluctuations 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 ∝1/N for the product of the correlation functions along the domain walls.