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The classical ground states of the SU(4) Heisenberg model on the facecentered cubic lattice constitute a highly degenerate manifold. We explicitlyconstruct all the classical ground states of the model. To describe quantumfluctuations above these classical states, we apply linear flavor-wave theory.At zero temperature, the bosonic flavor waves select the simplest of theseSU(4) symmetry breaking states, the four-sublattice ordered state defined bythe cubic unit cell of the fcc lattice. Due to geometrical constraints, flavorwaves interact along specific planes only, thus rendering the systemeffectively two dimensional and forbidding ordering at finite temperatures. Weargue that longer range interactions generated by quantum fluctuations canshift the transition to finite temperatures.

Order by disorder in a four flavor Mott-insulator on the fcc lattice