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 [20] and Ding-Eldan-Zhai [29], 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.