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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 $S_Φ(ω)\sim \vert 1+ {(ω/Ω)}^2\vert^{-α(T)/2}$, with $0.85\leq α(TDGL)(T)\leq 0.95$ and $1.17 \leq α(RSJ)(T) \leq 1.27$, 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.