Origin of anomalous magnetic noise from monopoles in $\mathrm{Dy_2Ti_2O_7}$

In $\mathrm{Dy_2Ti_2O_7}$ at $T$ of about 0.5 to 3 K the magnetization-noise spectrum follows $S(\omega) \sim \omega^{-b}$ with $b$ between 1 and 2, and relaxation is faster than Arrhenius would allow at high $T$ and slower at low $T$. Derive $b(T)$ and the relaxation time $\tau(T)$ from a microscopic dipolar model with monopole hopping, without free parameters beyond the fitted exchange set. An answer is a model reproducing $S(\omega, T)$ quantitatively.

Simulations of the fitted dipolar model with realistic monopole hopping that reproduce measured SQUID noise spectra across temperature.