2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187481This paper concludes our efforts in describing SU(3)-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Due to the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small.10 pages, 7 figuresHigh Energy Physics - LatticeHigh Energy Physics - Theorytext