  We show that quantum absorption refrigerators, which have traditionally been
studied as of three qubits, each of which is connected to a thermal reservoir,
can also be constructed by using three qubits and two thermal baths, where two
of the qubits, including the qubit to be locally cooled, are connected to a
common bath. With a careful choice of the system, bath, and qubit-bath
interaction parameters within the Born-Markov and rotating-wave approximations,
one of the qubits attached to the common bath achieves a cooling in the steady
state. We observe that the proposed refrigerator may also operate in a
parameter regime where no or negligible steady-state cooling is achieved, but
there is considerable transient cooling. The steady-state temperature can be
lowered significantly by an increase in the strength of the few-body
interaction terms existing due to the use of the common bath in the
refrigerator setup. The proposed refrigerator built with three qubits and two
baths is shown to provide steady-state cooling for both Markovian qubit-bath
interactions between the qubits and canonical bosonic thermal reservoirs, and a
simpler reset model for the qubit-bath interactions.
