  If Dark Matter halos possess the gravitational equivalent of an intrinsic
magnetic spin, a formal analogy exists between the low redshift behaviour of
the Cosmic Web in a flat FLRW background, and a crystal of spins submerged in a
thermal reservoir with temperature $T \propto H(t)$. We argue that, within the
use of the Bianchi type IX geometry to describe the gravitational collapse of
matter inhomogeneities, the spins are nothing but the heritage of its
underlying $SU(2)$ symmetry. Therefore, just like electrons in quantum
mechanics, these structures may have spin independently from their orbital
angular momentum. We explore the phenomenological implications on cosmological
scales of a possible late time phase transition of the Cosmic Web towards (the
gravitational equivalent of) a ferromagnetic state, described qualitatively
using the Ising model in the mean field approximation.
