Topological dynamics and dynamical scaling behavior of vortices in a two-dimensional XY model

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dc.creatorQi, Wei-Kai
dc.creatorChen, Yong
dc.date2008-09-02
dc.date.accessioned2026-07-07T09:59:56Z
dc.date.available2026-07-07T09:59:56Z
dc.descriptionBy using topological current theory we study the inner topological structure of vortices a two-dimensional (2D) XY model and find the topological current relating to the order parameter field. A scalar field, $ψ$, is introduced through the topological current theory. By solving the scalar field, the interaction energy of vortices in a 2D XY model is revisited. We study the dynamical evolution of vortices and present the branch conditions for generating, annihilating, crossing, splitting and merging of vortices. During the growth or annihilation of vortices, the dynamical scaling law of relevant length in a 2D XY model, $ξ(t)\propto(t-t^*)^{1/z}$, is obtained in the neighborhood of the limit point, given the dynamic exponent $z=2$. This dynamical scaling behavior is consistent with renormalization group theory, numerical simulations, and experimental results. Furthermore, it is found that during the crossing, splitting and merging of vortices, the dynamical scaling law of relevant length is $ξ(t)\propto(t-t^*)$. However, if vortices are at rest during splitting or merging, the dynamical scaling law of relevant length is a constat.
dc.description10 pages, 5 figures. any comments are favored
dc.identifierhttps://arxiv.org/abs/0809.0348
dc.identifierhttp://arxiv.org/abs/0809.0348
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168202
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleTopological dynamics and dynamical scaling behavior of vortices in a two-dimensional XY model
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