  We investigate the properties of the Gibbs states and thermodynamic
observables of the spherical model in a random field. We show that on the
low-temperature critical line the magnetization of the model is not a
self-averaging observable, but it self-averages conditionally. We also show
that an arbitrarily weak homogeneous boundary field dominates over fluctuations
of the random field once the model transits into a ferromagnetic phase. As a
result, a homogeneous boundary field restores the conventional self-averaging
of thermodynamic observables, like the magnetization and the susceptibility. We
also investigate the effective field created at the sites of the lattice by the
random field, and show that at the critical temperature of the spherical model
the effective field undergoes a transition into a phase with long-range
correlations $\sim r^{4-d}$.
