The uniformly frustrated two-dimensional XY model in the limit of weak frustration

Abstract

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behaviour of the XY model for T <= T_{KT}, where T_{KT} is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behaviour of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.

arXiv comment12 pages

References in corpus (10)

• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Multicritical behavior in the fully frustrated XY model and related systems
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Vortex Lattice Melting in 2D Superconducting Networks and Films
• Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field
• Flux lattice melting and depinning in the weakly frustrated 2D XY model
• Transitions and crossover phenomena in fully frustrated XY systems
• Patterns of Striped order in the Classical Lattice Coulomb Gas
• Bulk and surface properties in the critical phase of the two-dimensional XY model

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• Avoided criticality and slow relaxation in frustrated two dimensional models
• Uniformly frustrated XY model: strengthening of the vortex lattice by intrinsic disorder