Irrelevant operators and equivalent field theories

The model described by a given Lagrangian is studied in 1+1 dimensions. Wilson's renormalization prescription is adopted and a non-trivial infrared stable fixed point is obtained in the mean-field approximation. It is demonstrated that at the fixed point the operators used in the Lagrangian for n=4,6,...infinity become irrelevant and the theory becomes equivalent to the Gross-Neveu model. The equivalence is independent of the values of the dimensionless bare couplings of the original model (universality). Similar results are obtained in the case of other models in 3+1 dimensions. (Auth.)