2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174132We study the Gibbs measure of the nonhierarchical versions of the Generalized Random Energy Models introduced in previous work. We prove that the ultrametricity holds only provided some nondegeneracy conditions on the hamiltonian are met.Revised versionProbability60G60, 82B44text