  We investigate equilibrium statistical properties of the quantum XY spin-1/2
model in an external magnetic field when the interaction and field parts are
subjected to quenched or/and annealed disorder. The randomness present in the
system are termed annealed or quenched depending on the relation between two
different time scales - the time scale associated with the equilibriation of
the randomness and the time of observation. Within a mean-field framework, we
study the effects of disorders on spontaneous magnetization, both by
perturbative and numerical techniques. Our primary interest is to understand
the differences between quenched and annealed cases, and also to investigate
the interplay when both of them are present in a system. We observe in
particular that when interaction and field terms are respectively quenched and
annealed, critical temperature for the system to magnetize in the direction
parallel to the applied field does not depend on any of the disorders. Further,
an annealed disordered interaction neither affects the magnetizations nor the
critical temperatures. We carry out a comparative study of the different
combinations of the disorders in the interaction and field terms, and point out
their generic features.

Disordered Systems and Neural Networks;Statistical Mechanics;Quantum Physics