2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23213We investigate numerically the low temperature equilibration of glassy systems via non-local Monte Carlo methods. We re-examine several systems that have been studied previously and investigate new systems in order to test the performance of such methods near the putative Kauzmann temperature, $T_K$, where the configurational entropy is presumed to vanish. Our results suggest that previous numerical claims in favor of and against a thermodynamic transition at a finite $T_K$ must be re-evaluated. Our work provides some guidelines and suggestions for future numerical investigations of disordered systems at high densities and low temperatures.Submitted to J. Phys. Chem. B issue in honor of H.C. AndersenSoft Condensed MatterStatistical Mechanicstext