  We discuss the thermodynamic and finite size scaling properties of the
geometric phase in the adiabatic Dicke model, describing the super-radiant
phase transition for an $N$ qubit register coupled to a slow oscillator mode.
We show that, in the thermodynamic limit, a non zero Berry phase is obtained
only if a path in parameter space is followed that encircles the critical
point. Furthermore, we investigate the precursors of this critical behavior for
a system with finite size and obtain the leading order in the 1/N expansion of
the Berry phase and its critical exponent.
