2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184515In hep-th/0312197 a nonperturbative proof of the g-theorem of Affleck and Ludwig was put forward. In this paper we illustrate how the proof of hep-th/0312197 works on the example of the 2D Ising model at criticality perturbed by a boundary magnetic field. For this model we present explicit computations of all the quantities entering the proof including various contact terms. A free massless boson with a boundary mass term is considered as a warm-up example.1+20 pages, Latex, 2 eps figures; v2: references addedHigh Energy Physics - TheoryStatistical Mechanicstext