The dense vortex matter structure and associated magnetization are cal
culated for type-II superconducting mesoscopic disks. The magnetizatio
n exhibits generically first-order phase transitions as the number of
vortices changes by one and presents two well-defined regimes: A nonmo
notonous evolution of the magnitude of the magnetization jumps signals
the presence of a vortex glass structure which is separated by a seco
nd-order phase transition at H-c2 from a condensed state of vortices (
giant vortex) where the magnitude of the jumps changes monotonously. W
e compare our results with Hall magnetometry measurements by Geim et a
l. [Nature (London) 390, 259 (1997)] and claim that the magnetization
exhibits clear traces of the presence of these vortex glass states.