Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Letters A

The critical behavior of the 3D X-Y model and its relation with fractal properties of the vortex excitations

N.K. Kultanov, Yu. E. Lozovik

Published Dec 1, 1996• 2 citations
Publisher
DOI
10.1016/s0375-9601(96)00682-2

Related papers

Properties of vortex loops in the 3D XY model

Andrew V. Pochinsky, M.I. Polikarpov, B.N. Yurchenko

Physics Letters A•Apr 1, 1991•11 citations

Dynamical critical behavior of 3D S=1/2 XY model

M. Howard Lee

AIP conference proceedings•Jan 1, 1976•1 citation

Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model

Massimo Camarda, Fabio Siringo, R. Pucci +2 more

The geometric properties of critical fluctuations in the three-dimensional (3D) $XY$ model are analyzed. The 3D $XY$ model is a lattice model describing superfluids. We present a direct evaluation of the Hausdorff dimension ${D}_{H}$ of the vortex loops which are the critical fluctuations of the 3D $XY$ model. We also present analytical arguments for why $\ensuremath{\vartheta}$ in the scaling relation ${\ensuremath{\eta}}_{\ensuremath{\phi}}+{D}_{H}=2+\ensuremath{\vartheta}$ between ${D}_{H}$ and the anomalous scaling dimension of the corresponding field theory must be zero.

arXiv:cond-mat/0607830•Physical Review B•Sep 14, 2006•14 citations

Thermal quenches in the stochastic Gross-Pitaevskii equation: Morphology of the vortex network

Michikazu Kobayashi, Leticia F. Cugliandolo

We study the evolution of 3d weakly interacting bosons at finite chemical potential with the stochastic Gross-Pitaevskii equation. We fully characterise the vortex network in an out of equilibrium. At high temperature the filament statistics are the ones of fully-packed loop models. The vortex tangle undergoes a geometric percolation transition within the thermodynamically ordered phase. After infinitely fast quenches across the thermodynamic critical point deep into the ordered phase, we identify a first approach towards the critical percolation state, a later coarsening process that does not alter the fractal properties of the long vortex loops, and a final approach to equilibrium. Our results are also relevant to the statistics of linear defects in type II superconductors, magnetic materials and cosmological models.

arXiv:1606.03262•Europhysics Letters (EPL)•Jul 1, 2016•15 citations

1/f-flux-noise and dynamical critical properties of vortices in two-dimensional XY models

Johannes E. Van Himbergen, Paul H. E. Tiesinga, Jorge V. José +1 more

APS•Mar 1, 1997•0 citations

TOPOLOGICAL EXCITATIONS AND SECOND ORDER TRANSITIONS IN 3D O(N) MODELS

Luís M. A. Bettencourt

I discuss several examples of critical phenomena in O(N) models where topological excitations play an important role at criticality. I focus particular attention on the O(2) model in 3D, where recent measurements of the vortex string length distribution in equilibrium suggest the existence of a quantitative picture of the critical behavior in terms of defects. The compatibility of this perspective with renormalization group predictions is examined.

Topology of Strongly Correlated Systems•Aug 1, 2001•0 citations
The geometric properties of critical fluctuations in the three-dimensional (3D) XYXYXY model are analyzed. The 3D XYXYXY model is a lattice model describing superfluids. We present a direct evaluation of the Hausdorff dimension DH{D}_{H}DH​ of the vortex loops which are the critical fluctuations of the 3D XYXYXY model. We also present analytical arguments for why $\ensuremath{\vartheta}$ in the scaling relation ${\ensuremath{\eta}}_{\ensuremath{\phi}}+{D}_{H}=2+\ensuremath{\vartheta}$ between DH{D}_{H}DH​ and the anomalous scaling dimension of the corresponding field theory must be zero.
We study the evolution of 3d weakly interacting bosons at finite chemical potential with the stochastic Gross-Pitaevskii equation. We fully characterise the vortex network in an out of equilibrium. At high temperature the filament statistics are the ones of fully-packed loop models. The vortex tangle undergoes a geometric percolation transition within the thermodynamically ordered phase. After infinitely fast quenches across the thermodynamic critical point deep into the ordered phase, we identify a first approach towards the critical percolation state, a later coarsening process that does not alter the fractal properties of the long vortex loops, and a final approach to equilibrium. Our results are also relevant to the statistics of linear defects in type II superconductors, magnetic materials and cosmological models.