2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120797A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost surely. This includes all the known cases as well as some heavy-tailed distributions.10 pagesProbabilityMathematical Physics60F10; 82D30text