The Critical Exponents Of The Matrix Valued Gross-Neveu Model

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We study the large N limit of the MATRIX valued Gross-Neveu model in 2<d<4 dimensions. The method employed is a combination of the approximate recursion formula of Polyakov and Wilson with the solution to the zero dimensional large N counting problem of Makeenko and Zarembo. The model is found to have a phase transition at a finite value for the critical temperature and the critical exponents are approximated by nu = 1/(2(d-2)) and eta=d-2. We test the validity of the approximation by applying it to the usual vector models where it is found to yield exact results to leading order in 1/N.