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

TL;DR

This paper investigates the critical value of the improvement parameter in lattice Hamiltonian models with O(N) symmetry, using 1/N expansion to identify conditions where leading irrelevant operators decouple, reducing nonscaling effects.

Contribution

It introduces a systematic method to evaluate the critical improvement parameter in lattice Hamiltonian systems with O(N) symmetry using 1/N expansion.

Findings

Determines the critical improvement parameter γ* for vector spin models.

Provides asymptotic expansions for lattice massive one-loop integrals.

Shows decoupling of leading irrelevant operators at γ=γ*.

Abstract

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.