2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146499Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. The two models are simple variations of the classical paramagnetic spin model of non-interacting spins and are solved as easily as the latter model.v1: 11 pages, 5 figures. v2: Short, published version of v1, 6 pages, 3 figures. See v1 for the solutions of some of the problems listed in v2Statistical Mechanicstext