2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/38831This paper provides a technical companion to M. Aguado and E. Seiler, hep-lat/0406041, in which the fate of perturbation theory in the thermodynamic limit is discussed for the O(N) model on a 2d lattice and different boundary conditions. The techniques used to compute perturbative coefficients are explained, and results for all boundary conditions considered reviewed in detail.v2: plots reorganised, ref. updated, minor changes, 23 pages, 35 eps figures; v1: 22 pages, 41 eps figuresHigh Energy Physics - Latticetext