  It is shown here that $1/f^\alpha$ flux noise in conventional low-T$_c$
SQUIDs is a result of low temperature superparamagnetic phase transitions in
small clusters of strongly correlated color center defects. The spins in each
cluster interact via long-range ferromagnetic interactions. Due to its small
size, the cluster behaves like a 'random-telegraphic' macro-spin when
transitioning to the superparamagnetic phase. This results in $1/f^{\alpha}$
noise when ensemble averaged over a random distribution of clusters. This model
is self-consistent and explains all related experimental results which includes
$\alpha\sim 0.8$ independent of system-size. The experimental
flux-inductance-noise spectrum is explained through three-point correlation
calculations and time reversal symmetry breaking arguments. Also, unlike the
flux noise, it is shown why the second-spectrum inductance noise is inherently
temperature dependent due to the fluctuation-dissipation theorem. A
correlation-function calculation methodology using Ising-Glauber dynamics was
key for obtaining these results.
