  Phonon Casimir effect is the long-range interaction between impurities in
condensed matter systems, mediated by vacuum fluctuations of the phonon field.
For pairs of impurities, this interaction has been shown to follow a
quasi-power law at zero-temperature and evolve into an exponentially decaying
form as the temperature is increased. This work introduces an approach to deal
with systems of more than two impurities, both at zero and finite temperatures.
