Glassy Vortex State in a Two-Dimensional Disordered XY-Model

TL;DR

This paper investigates a two-dimensional disordered XY-model, revealing a glassy vortex phase with quasi long-range order, characterized by a non-reentrant transition and unique correlation behaviors, analyzed through a renormalization group approach.

Contribution

It introduces a renormalization group analysis of the disordered XY-model, identifying a glassy vortex phase and a new universality class of transition without replica symmetry breaking.

Findings

Existence of a glassy vortex phase with quasi long-range order

Identification of a non-reentrant transition of a new universality class

Correlation functions reveal a crossover line with non-analytic behavior

Abstract

The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered phase consists of a glass-like region at lower temperatures and of a non-glassy region at higher temperatures. The transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature. In contrast to previous approaches the disorder strength is found to be renormalized to larger values. Several correlation functions are calculated for the ordered phase. They allow to identify not only the transition into the glassy phase but also an additional crossover line, where the disconnected vortex correlation changes its behavior on large scales non-analytically. The renormalization group approach yields the glassy features without a breaking of replica symmetry.