1/ω Flux Noise and Dynamical Critical Properties of Two-DimensionalXYModels

We have numerically studied the dynamic correlation functions in thermodynamic equilibrium of two-dimensional O(2) symmetry models with either bond [resistively shunted Josephson (RSJ)] or site [time-dependent Ginsburg-Landau (TDGL)] dissipation as a function of temperature T. We find that above the critical temperature the frequency dependent flux noise S_Φ(ω)~|1+(ω/Ω)²|^-α(T)/2, with 0.85≤α(TDGL)(T)≤0.95 and 1.17≤α(RSJ)(T)≤1.27, while the dynamic critical exponents z(TDGL)~2.0 and z(RSJ)~0.9. Contrary to expectation the TDGL results are in closer agreement with the experiments in Josephson-junction arrays by Shaw et al. [Phys. Rev. Lett. 76, 2551 (1996)] than those from the RSJ model.