  We investigate the performance of a three-spin quantum absorption
refrigerator using a refined open quantum system model valid across all
inter-spin coupling strengths. It describes the transition between previous
approximate models for the weak and the ultrastrong coupling limit, and it
predicts optimal refrigeration for moderately strong coupling, where both
approximations are inaccurate. Two effects impede a more effective cooling: the
coupling between the spins no longer reduces to a simple resonant energy
exchange (the rotating wave approximation fails), and the interactions with the
thermal baths become sensitive to the level splitting, thus opening additional
heat channels between the reservoirs. We identify the modified conditions of
refrigeration as a function of the inter-spin coupling strength, and we show
that, contrary to intuition, a high-temperature work reservoir thwarts
refrigeration in the strong coupling regime.
