  We investigate the ensemble inequivalence of the spherical spin glass model
with nonlinear interactions of polynomial order $p$. This model is solved
exactly for arbitrary $p$ and is shown to have first-order phase transitions
between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$.
In the parameter region around the first-order transitions, the solutions give
different results depending on the ensemble used for the analysis. In
particular, we observe that the microcanonical specific heat can be negative
and the phase may not be uniquely determined by the temperature.

Statistical Mechanics;Disordered Systems and Neural Networks