  We study the depolarization dynamics of a dense ensemble of dipolar
interacting spins, associated with nitrogen-vacancy centers in diamond. We
observe anomalously fast, density-dependent, and non-exponential spin
relaxation. To explain these observations, we propose a microscopic model where
an interplay of long-range interactions, disorder, and dissipation leads to
predictions that are in quantitative agreement with both current and prior
experimental results. Our results pave the way for controlled many-body
experiments with long-lived and strongly interacting ensembles of solid-state
spins.
