  We investigate the energy landscape of the mixed even $p$-spin model with
Ising spin configurations. We show that for any given energy level between zero
and the maximal energy, with overwhelming probability there exist exponentially
many distinct spin configurations such that their energies stay near this
energy level. Furthermore, their magnetizations and overlaps are concentrated
around some fixed constants. In particular, at the level of maximal energy, we
prove that the Hamiltonian exhibits exponentially many orthogonal peaks. This
improves the results of Chatterjee and Ding-Eldan-Zhai, where the former
established a logarithmic size of the number of the orthogonal peaks, while the
latter proved a polynomial size. Our second main result obtains disorder chaos
at zero temperature and at any external field. As a byproduct, this implies
that the fluctuation of the maximal energy is superconcentrated when the
external field vanishes and obeys a Gaussian limit law when the external field
is present.
