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

Abstract

In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value ${\gamma }^{\ast }$ may exist such that, when $\gamma ={\gamma }^{\ast }$, 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 ${\gamma }^{\ast }$ 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.

Conclusions clarified; 26 pages, 6 figures, RevTeX 4