  With Monte Carlo methods we study the dynamic relaxation of a vortex state at
the Kosterlitz-Thouless phase transition of the two-dimensional XY model. A
local pseudo-magnetization is introduced to characterize the symmetric
structure of the dynamic systems. The dynamic scaling behavior of the
pseudo-magnetization and Binder cumulant is carefully analyzed, and the
critical exponents are determined. To illustrate the dynamic effect of the
topological defect, similar analysis for the the dynamic relaxation with a
spin-wave initial state is also performed for comparison. We demonstrate that a
limited amount of quenched disorder in the core of the vortex state may alter
the dynamic universality class. Further, theoretical calculations based on the
long-wave approximation are presented.
