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Abstract
We present a finite temperature Monte Carlo study of the XY-model
in the vortex representation, and study its dynamical critical
behavior
in two limits. The first neglects
magnetic field fluctuations, corresponding to the absence of
screening, which should be a good approximation
in high $T_c$ superconductors ($\kappa\to \infty$)
except extremely close to the critical point.
Here, from finite size scaling of the linear resistivity
we find the dynamical critical exponent of the vortex motion to be
$z\approx 1.5$. The second limit includes magnetic field
fluctuations in the strong screening limit ($\kappa\to 0$)
corresponding to the true asymptotic inverted XY critical regime, where
we find the unexpectedly large value $z\approx 2.7$.
We compare these
results, obtained from dissipative dynamics in the vortex representation,
with the universality class of the corresponding model in the phase
representation with propagating (spin wave) modes.
We also discuss the effect of disorder and the
relevance of our results for experiments.
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