Scaling laws and triviality bounds in the lattice Φ4 theory. Pt. 3

Our previous analytic treatment of the one-component standard lattice Φ4 theory in four dimensions is extended to the O(n) symmetric model. Particular attention is paid to the phenomenologically interesting case of n=4. The renormalization group trajectories in the symmetric and in the Goldstone phase are mapped out and bounds on the renormalized self-coupling as a function of the ultra-violet cutoff are determined. Since the import of the results obtained has already been discussed in detail elsewhere, the emphasis here is put on the technical aspects of our work. (orig.)