  We consider weakly interacting diffusions on the torus, for multichromatic
interaction potentials. We consider interaction potentials that are not
H-stable, leading to phase transitions in the mean field limit. We show that
the mean field dynamics can exhibit multipeak stationary states, where the
number of peaks is related to the number of nonzero Fourier modes of the
interaction. We also consider the effect of a confining potential on the
structure of non-uniform steady states. We approach the problem by means of
analysis, perturbation theory and numerical simulations for the interacting
particle systems and the PDEs.
