1/ω-flux-noise and dynamical critical properties of two-dimensional XY-models

We have numerically studied the dynamic correlation functions in thermodynamic equilibrium of two-dimensional O(2)-symmetry models with either bond (RSJ) or site (TDGL) dissipation as a function of temperature T. We find that above the critical temperature the frequency dependent flux noise $S_{\Phi}(\omega)\sim \vert 1+ {(\omega/\Omega)}^2\vert^{-\alpha (T)/2}$, with $0.85\leq \alpha (TDGL)(T)\leq 0.95$ and $1.17 \leq \alpha (RSJ)(T) \leq 1.27$, while the dynamic critical exponents $z(TDGL)\sim 2.0$ and $z(RSJ)\sim 0.9$. Contrary to expectation the TDGL results are in closer agreement with the experiments in Josephson-junction arrays by Shaw et al., than those from the RSJ model. We find that these results are related to anomalous vortex diffusion through vortex clusters.