  The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant
scalar field theories in $d$ dimensions is studied by applying the 1/N
expansion and strong coupling analysis. The O(1/N) correction to the
$\beta$-function and to the fixed point value $g_r^*$ are explictly computed.
Strong coupling series for lattice non-linear sigma models are analyzed near
criticality in d=2 and d=3 for several values of $N$ and the corresponding
values of $g_r^*$ are extracted. Large-N and strong coupling results are
compared with each other, finding a good general agreement. For small N the
strong coupling analysis in 2-d gives the best determination of $g^*_r$ to date
(or comparable for N=2,3 with the available Monte Carlo estimates), and in 3-d
it is consistent with available $\phi^4$ field theory results.
