Scaling laws and triviality bounds in the lattice $\phi$4 theory (III). n-component model

Our previous analytic treatment of the one-component standard lattice ϕ$^4$ 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