The critical exponents of the matrix-valued Gross-Neveu model Original Research Article

We study the large-N limit of the matrix-valued Gross-Neveu model in d > 2 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 ν = 1/(2(d − 2)) and η = 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.