  While macroscopic properties of spin glasses have been thoroughly
investigated, their manifestation in the corresponding microscopic
configurations is much less understood. Cases where both descriptions have been
provided, such as constraint satisfaction problems, are limited to their ground
state properties. To identify the emerging microscopic structures with
macroscopic phases at different temperatures, we study the $p$-spin model with
$p\!=\!3$. We investigate the properties of self-sustained clusters, defined as
variable sets where in-cluster induced fields dominate over the field induced
by out-cluster spins, giving rise to stable configurations with respect to
fluctuations. We compute the entropy of self-sustained clusters as a function
of temperature and their sizes. In-cluster fields properties and the difference
between in-cluster and out-cluster fields support the observation of
slow-evolving spins in spin models. The findings are corroborated by
observations in finite dimensional lattices at low temperatures.
