2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/176204We apply the generalized uncertainty principle to the thermodynamics of a small black hole. Here we have a black hole system with the UV cutoff. It is shown that the minimal length induced by the GUP interrupts the Gross-Perry-Yaffe phase transition for a small black hole. In order to see whether the black hole remnant takes place a transition to a large black hole, we introduce a black hole in a cavity (IR system). However, we fail to show the phase transition of the remnant to the large black hole.11 pages, 4 eps.figures, version to appear in PLBGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext