I would like to understand the reason behind the vanishing critical mass exponents. I've written a program that calculates the fixed points and then the eigenvalues corresponding to the fixed point solutions by substituting them into the Jacobian matrix where each term is composed of the partial derivatives of the beta functions with respect to the dimensionless couplings.
In d=3 scalar phi^4 model, I had no problem obtaining the critical exponents until N=5 but for N=6,7,8 I got just the trivial solutions due to the coupling fixed points being only zeros then for N=9 I got a sensible result for the critical exponent. I wonder whats happening between N=6 to N=8.