Evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena

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.