Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological dynamics and dynamical scaling behavior of vortices in a
  two-dimensional 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, $\psi$, 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, $\xi(t)\propto(t-t^*)^{1/z}$, 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 $\xi(t)\propto(t-t^*)$. However, if vortices are at
rest during splitting or merging, the dynamical scaling law of relevant length
is a constat.

29
The categories of this paper are: funct-an
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom