Nonabelian ferromagnets with three-body interactions

We study the thermodynamics of nonabelian ferromagnets consisting of atoms in the fundamental representation of $SU(N)$ and interacting with two-body and three-body interactions. Using a mean field approach, we uncover an intricate phase structure, depending on the relative strength and sign of the two-body and three-body coupling constants. In the case where two-body interactions are ferromagnetic and three-body ones are antiferromagnetic, we uncover a rich cascade of phase transitions, the appearance of phases with two distinct polarization directions being the most striking novel feature. Our results are relevant to magnetic systems where higher-body interactions cannot be neglected.