  We show that the limiting ground state energy of the spherical mixed p-spin
model can be identified as the infimum of certain variational problem. This
complements the well-known Parisi formula for the limiting free energy in the
spherical model. As an application, we obtain explicit formulas for the
limiting ground state energy in the replica symmetry, one level of replica
symmetry breaking and full replica symmetry breaking phases at zero
temperature. In addition, our approach leads to new results on disorder chaos
in spherical mixed even p-spin models. In particular, we prove that when there
is no external field, the location of the ground state energy is chaotic under
small perturbations of the disorder. We also establish that in the spherical
mixed even p-spin model, the ground state energy superconcentrates in the
absence of external field, while it obeys a central limit theorem if the
external field is present.
