2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112247We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of the present proposal is the possibility of performing a suitable description of microcanonical thermodynamic states during the first-order phase transitions by using this local Monte Carlo algorithm.RevTex, 4 pages + 1 eps figure, Revised versionStatistical Mechanicstext