  We consider the spherical mixed $p$-spin models and investigate the structure
of the Parisi measure at zero temperature. We prove that for the spherical spin
models with $n$ components, the Parisi measure at zero temperature is at most
$n$-RSB or $n$-FRSB. We also provide a necessary and sufficient computational
criterion for the spherical mixed $p$-spin model to be $k$-RSB or $k$-FRSB, $k
\leq n.$
