  We calculate numerically the fidelity and its susceptibility for the ground
state of the Dicke model. A minimum in the fidelity identifies the critical
value of the interaction where a quantum phase crossover, the precursor of a
phase transition for finite number of atoms N, takes place. The evolution of
these observables is studied as a function of N, and their critical exponents
evaluated. Using the critical exponents the universal curve for the specific
susceptibility is recovered. An estimate to the precision to which the ground
state wave function is numerically calculated is given, and found to have its
lowest value, for a fixed truncation, in a vicinity of the critical coupling.
