Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors

Abstract

As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. We suggest that for $d=3$ the simulation data are consistent with a topological phase transition at a nonzero critical field, $H_c$, to a pinned phase that is defect-free at large length-scales. We also discuss the connection between the possible existence of this phase transition in the random-field XY model and the magnetic field driven transition from pinned vortex lattice to vortex glass in weakly disordered type-II superconductors.

LATEX file; 5 Postscript figures are available from [email protected]

Cited by in corpus (82)

• Realizing the $XY$ Hamiltonian in polariton simulators
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Irreversibility, Mechanical Entanglement and Thermal Melting in Superconducting Vortex Crystals with Point Impurities
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Muon spin rotation and relaxation in magnetic materials
• A Bragg glass phase in the vortex lattice of a type II superconductor
• Theory of the striped superconductor
• Vortex Dynamics and Defects in Simulated Flux Flow
• Topological Order in the Vortex Glass Phase of High-Temperature Superconductors
• Anomalous Peak Effect in CeRu2 and NbSe2 : Fracturing of a Flux Line Lattice?
• Wigner Glass, Spin-liquids, and the Metal-Insulator Transition
• Disorder in quantum many-body systems
• Effects of dissipation on quantum phase transitions
• Pinning-induced transition to disordered vortex phase in layered superconductors
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• From stripe to checkerboard order on the square lattice in the presence of quenched disorder
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• Absence of Two-Dimensional Bragg Glasses
• Vortices Freeze like Window Glass: the Vortex Molasses Scenario
• Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors
• Phase Behavior of Type-II Superconductors with Quenched Point Pinning Disorder: A Phenomenological Proposal
• Peak Effect, Fishtail Effect and Plateau Effect : The Reentrant Amorphization of Vortex Matter in 2H-NbSe_2
• Fate of the Peak Effect in a Type-II Superconductor: Multicriticality in the Bragg-Glass Transition
• Topological Order in the Phase Diagram for High-Temperature Superconductors with Point Defects
• Theory of magnetic skyrmion glass
• Disordered Type-II Superconductors: A Universal Phase Diagram for Low-T${}_c$ Systems
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Glass phase of two-dimensional triangular elastic lattices with disorder
• Random Field XY Model in Three Dimensions
• Multiparticle ring exchange in the Wigner glass and its possible relevance to strongly interacting two-dimensional electron systems in the presence of disorder
• Disorder Induced Suppression of CDW Long Range Order: STM Study of Pd-intercalated ErTe3
• The Superfluid Glass Phase of 3He-A
• Dislocations and Bragg glasses in two dimensions
• Random Fields, Topology, and The Imry-Ma Argument
• Smectic Liquid Crystals in an Anisotropic Random Environment
• Amorphization of Vortex Matter and Reentrant Peak Effect in YBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Quasi-Long-Range Order in Random-Anisotropy Heisenberg Models
• Chaos and plasticity in superconductor vortices: a low-dimensional dynamics
• Fragile superconductivity in the presence of weakly disordered charge density waves
• Hysteretic behavior of the vortex lattice at the onset of the second peak for HgBa${}_2$CuO${}_{4+\delta }$ superconductor
• Nonuniversal Correlations and Crossover Effects in the Bragg-Glass Phase of Impure Superconductors
• Non-Universal Quasi-Long Range Order in the Glassy Phase of Impure Superconductors
• Analytical solution for multisingular vortex Gaussian beams: The mathematical theory of scattering modes
• A variational study of the random-field XY model
• A New Disorder Driven Roughening Transition of CDW's and Flux Line Lattices
• Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of $YN{i}_2{B}_{2}C$ and $LuN{i}_2{B}_{2}C$
• Bragg glass signatures in Pd${}_x$ErTe${}_3$ with X-ray diffraction Temperature Clustering (X-TEC)
• Spin and pair density wave glasses
• Ordered magnetism in the intrinsically decorated $j{}_{\mathrm{eff}}$ = $\frac{1}{2}$ $\alpha$-CoV${}_3$O${}_8$
• Topological order generated by random field in a 2D exchange model
• Critical Hysteresis in Random Field XY and Heisenberg Models
• Amorphous Vortex Glass Phase in Strongly Disordered Superconductors
• On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3
• Structure Factor of the 3D Random Field XY Model
• Vortex lines in the three-dimensional XY model with random phase shifts
• Domain Growth and Aging in the Random Field XY Model: A Monte Carlo Study
• Coupled two-component atomic gas in an optical lattice
• Vortex Phase Diagram of weakly pinned YBa${}_2$Cu${}_3$O${}_{7-\delta }$ for H $\parallel$ c
• Vortex Phase Diagram of Layered Superconductor Cu0.03TaS2 for H || c
• Ordered vs Disordered States of the Random-Field Model in Three Dimensions
• Random Field XY Model in Three Dimensions: The Role of Vortices
• Non-equilibrium quasi-long-range order of driven random field O(N) model
• Effect of Dilute Random Field on Continuous-Symmetry Order Parameter
• Dimensional reduction and its breakdown in the driven random field O(N) model
• Bragg- and Moving-glasses: a theory of disordered vortex lattices
• Quasi-long range order in the random anisotropy Heisenberg model
• Flux-lattice melting in two-dimensional disordered superconductors
• Interplay between pair density waves and random field disorders in the pseudogap regime of cuprate superconductors
• Planar pinning induced, lowering of vortex dimensionality and low field melting in a single crystal of Ba0.6K0.4Fe2As2
• Nonequilibrium Kosterlitz-Thouless transition in a three-dimensional driven disordered system
• Driven flux-line lattices in the presence of weak random columnar disorder: Finite-temperature behavior and dynamical melting of moving Bose glass
• Elasticity, fluctuations and vortex pinning in ferromagnetic superconductors: A "columnar elastic glass"
• Effect of dilute, strongly pinning impurities on charge density waves
• Coulombian Disorder in Periodic Systems
• Energy minima and ordering in ferromagnets with quenched randomness
• Smectic vortex glass
• The Smectic $A$-$C$ Phase Transition in Biaxial Disordered Environments
• Loss-driven gain enhancements driven by topological singularities in non-Hermitian photonic crystals defects
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Strange metal and Fermi arcs from disordering spin stripes
• Behavior of the Random Field $XY$ Model on Simple Cubic Lattices at $h_r=1.5$