  We prove the existence of a critical regime for the fluctuations of the
ground-state energy of the spherical Sherrington-Kirkpatrick model in an
external field, confirming predictions given in [3,12]. We also establish a
critical regime for the fluctuations in a model with a critical Ferromagnetic
interaction term, producing a three-parameter family of distributions
generalizing the two-parameter family given in [4]. These results are both
established in the generality of a $\beta$-ensemble analogue of the spherical
Sherrington-Kirkpatrick model, which subsumes the complex and quarternionic
generalizations.
