  We have developed a tunable colloidal system and a corresponding simulation
model for studying the phase behavior of particles assembling under the
influence of long-range magnetic interactions. A monolayer of paramagnetic
particles is subjected to a spatially uniform magnetic field with a static
perpendicular component and rapidly rotating in-plane component. The sign and
strength of the interactions vary with the tilt angle $\theta$ of the rotating
magnetic field. For a purely in-plane field, $\theta=90^{\circ}$, interactions
are attractive and the experimental results agree well with both equilibrium
and out-of-equilibrium predictions based on a two-body interaction model. For
tilt angles $50^{\circ}\lesssim \theta\lesssim 55^{\circ}$, the two-body
interaction gives a short-range attractive and long-range repulsive (SALR)
interaction, which predicts the formation of equilibrium microphases. In
experiments, however, a different type of assembly is observed. Inclusion of
three-body (and higher-order) terms in the model does not resolve the
discrepancy. We thus further characterize the anomalous behavior by measuring
the time-dependent cluster size distribution.
