PACS. 03.65.Ud -Entanglement and quantum nonlocality. PACS. 73.43.Nq -Quantum phase transitions. PACS. 75.10.-b -General theory and models of magnetic ordering.Abstract. -We show that the quantum phase transition arising in a standard radiationmatter model (Dicke model) belongs to the same universality class as the infinitely-coordinated, transverse field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.Quantum phase transitions (QPTs) are associated with a dramatic change in the physical properties of a system at zero temperature when a parameter varies around its critical value. It is well-known that very different systems can exhibit similar behavior in this critical regime, giving rise to the concept of universality. Enlarging a given universality class by the addition of systems from very different areas of physics, is a very important step toward unifying our understanding of the basic physics underlying apparently disconnected complex phenomena. Recently there have been studies of light-controlled condensed matter systems displaying QPTs with atoms in extreme one-dimensional confinements [1], ions driven by properly tuned and pulsed light [2] and fermionic atoms in optical superlattices [3]. Fully quantum mechanical models of radiation-matter systems are also being considered, and are important for several reasons: Scalable and distributed quantum information processing (QIP) devices will demand the integration of matter quantum bits (qubits) such as atoms, trapped ions, semiconductor quantum dots or SQUIDs with photons. In addition, the capability of photons to control and modify the coupling between physically distant qubits makes them appropriate for manipulating and transferring quantum information.