  Clusters of interacting two-level-systems (TLS),likely due to $F^+$ centers
at the metal-insulator interface, are shown to self consistently lead to
$1/f^{\alpha }$ magnetization noise in SQUIDs. By introducing a
correlation-function calculation method and without any a priori assumptions on
the distribution of fluctuation rates, it is shown why the flux noise is only
weakly temperature dependent with $\alpha\lesssim 1$, while the inductance
noise has a huge temperature dependence seen in experiment, even though the
mechanism producing both spectra is the same. Though both ferromagnetic- RKKY
and short-range-interactions (SRI) lead to strong flux-inductance-noise
cross-correlations seen in experiment, the flux noise varies a lot with
temperature for SRI. Hence it is unlikely that the TLS's time reversal symmetry
is broken by the same mechanism which mediates surface ferromagnetism in
nanoparticles and thin films of the same insulator materials.
