XY models with disorder and symmetry-breaking fields in two dimensions

TL;DR

This paper investigates how disorder and symmetry-breaking fields influence the phase behavior of the two-dimensional XY model, revealing a modified phase diagram with diverse ordered phases using a renormalization group approach.

Contribution

It introduces a comprehensive analysis of disorder effects on the XY model's phase diagram, highlighting differences from previous special-case studies through a Coulomb gas and renormalization group approach.

Findings

Identification of phases with long-range, quasi-long-range, and short-range order.

Discovery of a changed phase diagram topology due to disorder.

Breakdown of the fugacity expansion in the Coulomb gas representation.

Abstract

The combined effect of disorder and symmetry-breaking fields on the two-dimensional XY model is examined. The study includes disorder in the interaction among spins in the form of random phase shifts as well as disorder in the local orientation of the field. The phase diagrams are determined and the properties of the various phases and phase transitions are calculated. We use a renormalization group approach in the Coulomb gas representation of the model. Our results differ from those obtained for special cases in previous works. In particular, we find a changed topology of the phase diagram that is composed of phases with long-range order, quasi-long-range order, and short-range order. The discrepancies can be ascribed to a breakdown of the fugacity expansion in the Coulomb gas representation. Implications for physical systems such as planar Josephson junctions and the faceting of crystal surfaces are discussed.