  We perform spin noise spectroscopy close to resonance in a 1-mm-thick cell
containing a dense Rubidium vapor. A laser is used to excite optical dipoles in
the vapor while probing the Faraday rotation noise. We report unusual
lineshapes of the spin noise spectra with a strong density dependence, which we
attribute to interactions arising between particles in the system. Introducing
a two-body model and simulations, we show that these features are the hallmark
of a strong dipole-dipole interaction between binaries within the ensemble. A
precise fit of the experimental spectra allows to extract the strength and the
duration of the dipole-dipole interaction. We unveil its impact on the spin
noise frequency and investigate the role of the atomic motion in the unexpected
lineshapes. This work demonstrates the potential of spin noise spectroscopy to
observe and quantify strong interactions occurring within a particle ensemble.
