  In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical
value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading
irrelevant operator decouples from the Hamiltonian and the leading nonscaling
contribution to renormalization-group invariant physical quantities (evaluated
in the critical region) vanishes. The 1/N expansion technique is applied to the
evaluation of $\gamma^*$ for the lattice Hamiltonian of vector spin models with
O(N) symmetry. As a byproduct, systematic asymptotic expansions for the
relevant lattice massive one-loop integrals are obtained.
