Identifying the order of a quantum phase transition by means of Wehrl entropy in phase-space

We propose a method to identify the order of a Quantum Phase Transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the Quantum Cusp, and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.