  We study the Ising pure $p$-spin model for large $p$. We investigate the
landscape of the Hamiltonian of this model. We show that for any $\gamma>0$ and
any large enough $p$, the model exhibits an intricate geometrical property
known as the multi Overlap Gap Property above the energy value
$\gamma\sqrt{2\ln 2}$. We then show that for any inverse temperature $\sqrt{\ln
2}<\beta<\sqrt{2\ln 2}$ and any large $p$, the model exhibits shattering:
w.h.p. as $n\to\infty$, there exists exponentially many well-separated clusters
such that (a) each cluster has exponentially small Gibbs mass, and (b) the
clusters collectively contain all but a vanishing fraction of Gibbs mass.
Moreover, these clusters consist of configurations with energy near $\beta$.
Range of temperatures for which shattering occurs is within the replica
symmetric region. To the best of our knowledge, this is the first shattering
result regarding the Ising $p$-spin models. Our proof is elementary, and in
particular based on simple applications of the first and the second moment
methods.
