Deconfinement transitions in a generalised XY model

Abstract

We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices and ordinary vortices, as well as an Ising-type transition. There also occurs an unusual deconfining phase transition, where the disordered to superfluid transition is of Ising rather than KT type. We show by analytical arguments and extensive numerical simulations that there is a point in the phase diagram where the KT transition line meets the deconfining Ising phase transition. We find that the latter extends into the disordered phase not as a phase transition, but rather solely as a deconfinement transition. It is best understood in the dual height model, where on one side of the transition height steps are bound into pairs while on the other they are unbound. We also extend the phase diagram of the dual model, finding both O(2) loop model and antiferromagnetic Ising transitions.

19 pages. v2: references added and minor changes. Appears in "John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday"

References in corpus (12)

• "Deconfined" quantum critical points
• Worm algorithms for classical statistical models
• The superconductor-insulator transition in 2D dirty boson systems
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Superfluid transitions in bosonic atom-molecule mixtures near Feshbach resonance
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• Superfluidity and phase transitions in a resonant Bose gas
• New ordered phases in a class of generalized XY models
• Boson pairing and unusual criticality in a generalized XY model
• Directed geometrical worm algorithm applied to the quantum rotor model
• Competing nematic interactions in a generalized XY model in two and three dimensions
• Kosterlitz-Thouless and Potts transitions in a generalized XY model

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• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
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• Multiversality and Unnecessary Criticality in One Dimension
• Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks
• $XY$ model with antinematic interaction
• Phase diagram of generalized XY model using tensor renormalization group
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Vortex confinement transitions in the modified Goldstone model
• Classical origins of Landau-incompatible transitions
• ${\mathbb{Z}}_n$ modified XY and Goldstone models and vortex confinement transition
• Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems
• Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction
• Two-stage melting of an inter-component Potts long-range order in two dimensions
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models