Vortices in the 2-dimensional-s = 1/2-xy model

By 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.By 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.

arXiv:0809.0348Sep 2, 20080 citations

Vortices in the two-dimensional s=1/2XY model

Donald D. Betts, F. C. Salevsky, Jos Rogiers

Operators are derived for the vortex density and the vortex-antivortex pair density of s= 1 / 2 models on the square and triangular lattices. At T=0 the finite-lattice method estimates of the number of vortices and antivortices per plaquette for the XY model are 0.025+or-0.002 for the square lattice and 0.052+or-0.008 for the triangular lattice. High-temperature series expansions on the triangular lattice allow the vortex and pair densities of the XY model to be plotted against inverse temperature.Operators are derived for the vortex density and the vortex-antivortex pair density of s= 1 / 2 models on the square and triangular lattices. At T=0 the finite-lattice method estimates of the number of vortices and antivortices per plaquette for the XY model are 0.025+or-0.002 for the square lattice and 0.052+or-0.008 for the triangular lattice. High-temperature series expansions on the triangular lattice allow the vortex and pair densities of the XY model to be plotted against inverse temperature.

Journal of Physics A Mathematical and GeneralFeb 1, 198118 citations

Superfluid Vortices

Lucy J. Campbell

ScienceDec 6, 19910 citations

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.