  The Husimi distribution is proposed for a phase space analysis of quantum
phase transitions in the Dicke model of spin-boson interactions. We show that
the inverse participation ratio and Wehrl entropy of the Husimi distribution
give sharp signatures of the quantum phase transition. The analysis has been
done using two frameworks: a numerical treatment and an analytical variational
approximation. Additionally we have proposed a new characterization of the
Dicke model quantum phase transition by means of the zeros of the Husimi
distribution in the variational approach.
