  Statistical mechanics underlies our understanding of macroscopic quantum
systems. It is based on the assumption that out-of-equilibrium systems rapidly
approach their equilibrium states, forgetting any information about their
microscopic initial conditions. This fundamental paradigm is challenged by
disordered systems, in which a slowdown or even absence of thermalization is
expected. We report the observation of critical thermalization in a three
dimensional ensemble of $\sim 10^6$ electronic spins coupled via dipolar
interactions. By controlling the spin states of nitrogen vacancy color centers
in diamond, we observe slow, sub-exponential relaxation dynamics and identify a
regime of power-law decay with disorder-dependent exponents; this behavior is
modified at late times owing to many-body interactions. These observations are
quantitatively explained by a resonance counting theory that incorporates the
effects of both disorder and interactions.
