  We study the conditions for spontaneous symmetry breaking of the
(2+1)-dimensional noncommutative phi^6 model in the small-theta limit. In this
regime, considering the model as a cutoff theory, it is reasonable to assume
translational invariance as a property of the vacuum state and study the
conditions for spontaneous symmetry breaking by an effective potential
analysis. An investigation of up to the two loop level reveals that
noncommutative effects can modify drastically the shape of the effective
potential. Under reasonable conditions, the nonplanar sector of the theory can
become dominant and induce symmetry breaking for values of the mass and
coupling constants not reached by the commutative counterpart.
