On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena

Abstract

In lattice Hamiltonian systems with a quartic coupling $γ$, a critical value $γ^*$ may exist such that, when $γ=γ^*$, 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 $γ^*$ 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.