Destruction of bulk ordering by surface randomness

TL;DR

Surface randomness in systems with continuous symmetry can eliminate bulk long-range order, leading to quasi-long range order, with exact correlation functions derived for XY models using functional renormalization group analysis.

Contribution

This paper provides exact calculations of correlation functions for XY models with surface disorder and reveals the persistence of topological order in three dimensions despite strong surface randomness.

Findings

Surface disorder destroys bulk long-range order in continuous symmetry systems.

Quasi-long range order replaces long-range order due to surface randomness.

Topological order persists in 3D XY models even with strong surface disorder.

Abstract

We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long range order in the bulk, and, instead, quasi-long range order emerges. Correlation functions are calculated exactly for the two- and three-dimensional XY model with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder.