Phase transition in SU(N) symmetric models for the adjoint field φ in the case of arbitrary N is investigated. We examine the fluctuation-induced symmetry breaking from the point of view of the ferromagnetic phase transition in the large spin Fermi system, where the order parameter 〈φ〉 occurs discontinuously for N≥4. The free energies of the systems are analyzed within both ε-expansion and the functional renormalization group.