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A three-dimensional O(N) model with both fermions and scalar bosons are studied extensively up to the second order in the 1/ N expansion. Fermionic interactions work towards stabilizing the vacuum as seen from the Gaussian variational method. Vacuum stability requires a constraint among dimensionless coupling constants. The effective potential is calculated up to the second order. Renormalizing the effective potential, we calculate the renormalization-group functions. There are some fixed points. The renormalization-group flow diagram shows that there exists an ultraviolet stable fixed point compatible with the vacuum stability constraint. The fixed point corresponding to that in the supersymmetric limit is seen to be unstable unless there is an exact supersymmetry from the beginning.

A Nontrivial Ultraviolet Fixed Point and Stability of Three-Dimensional O(N) Model with Fermions and Bosons