  Motivated by two different types of disorder that occur in quantum systems
with ubiquity, namely, the random and the quasiperiodic (QP) disorder, we have
performed a systematic comparison of the emerging phase properties
corresponding to these two cases for a system of interacting bosons in a two
dimensional square lattice. Such a comparison is imperative as a random
disorder at each lattice is completely uncorrelated, while a quasiperiodic
disorder is deterministic in nature. Using a site decoupled mean-field
approximation followed by a percolation analysis on a BoseHubbard model,
several different phases are realized, such as the familiar Bose-glass (BG),
Mott insulator (MI), superfluid (SF) phases, and, additionally, we observe a
mixed phase, specific to the QP disorder, which we call as a QM phase.
Incidentally, the QP disorder stabilizes the BG phase more efficiently than the
case of random disorder. Further, we have employed a finite-size scaling
analysis to characterize various phase transitions via computing the critical
transition points and the corresponding critical exponents. The results show
that for both types of disorder, the transition from the BG phase to the SF
phase belongs to the same universality class. However, the QM to the SF
transition for the QP disorder comprises of different critical exponents,
thereby hinting at the involvement of a different universality class therein.
The critical exponents that depict all the various phase transitions occurring
as a function of the disorder strength are found to be in good agreement with
the quantum Monte-Carlo results available in the literature.
