  We explore a small quantum refrigerator in which the working substance is
made of paradigmatic nearest-neighbor quantum spin models, the XYZ and the XY
model with Dzyaloshinskii-Moriya interactions, consisting of two and three
spins, each of which is in contact with a bosonic bath. We identify a specific
range of interaction strengths which can be tuned appropriately to ensure a
cooling of the selected spin in terms of its local temperature in the
weak-coupling limit. Moreover, we report that in this domain, when one of the
interaction strengths is disordered, the performance of the thermal machine
operating as a refrigerator remains almost unchanged instead of degradation,
thereby establishing the flexibility of this device. However, to obtain a
significant amount of cooling via ordered as well as disordered spin models, we
observe that one has to go beyond the weak-coupling limit and compute the
figures of merits by using global master equations.
