  The grand canonical formalism is employed to study the thermodynamic
structure of a model displaying a quantum phase transition when studied with
respect to the canonical formalism. A numerical survey shows that the grand
partition function diverges following a power law when the interaction
parameter approaches a limiting constant. The power-law exponent takes a
distinctive value when such limiting constant coincides with the critical point
of the subjacent quantum phase transition. An approximated expression for the
grand partition function is derived analytically implementing a mean field
scheme and a number of thermodynamic observables are obtained. The system
observables show signatures that can be used to track the critical point of the
underlying transition. This result provides a simple fact that can be exploited
to verify the existence of a quantum phase transition avoiding the zero
temperature regime.
