  Academic research groups are treated as complex systems and their cooperative
behaviour is analysed from a mathematical and statistical viewpoint. Contrary
to the naive expectation that the quality of a research group is simply given
by the mean calibre of its individual scientists, we show that intra-group
interactions play a dominant role. Our model manifests phenomena akin to phase
transitions which are brought about by these interactions, and which facilitate
the quantification of the notion of critical mass for research groups. We
present these critical masses for many academic areas. A consequence of our
analysis is that overall research performance of a given discipline is improved
by supporting medium-sized groups over large ones, while small groups must
strive to achieve critical mass.
