  The random field Curie-Weiss model is derived from the classical Curie-Weiss
model by replacing the deterministic global magnetic field by random local
magnetic fields. This opens up a new and interestingly rich phase structure. In
this setting, we derive moderate deviations principles for the random total
magnetization $S_n$, which is the partial sum of (dependent) spins. A typical
result is that under appropriate assumptions on the distribution of the local
external fields there exist a real number $m$, a positive real number
$\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies
a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate
function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.
