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We investigate whether the beta function of the finite-$N$ Gross-Neveu model,as calculated up to the four-loop level, exhibits evidence for an infraredzero. As part of our analysis, we calculate and analyze Pad\'e approximants tothis beta function and evaluate effects of scheme dependence. From our study,we find that in the range of coupling where the perturbative calculation of thefour-loop beta function is reliable, it does not exhibit robust evidence for aninfrared zero.

On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model