  We propose a scheme in which the Lipkin-Meshkov-Glick model is realized
within a circuit QED system. An array of N superconducting qubits interacts
with a driven cavity mode. In the dispersive regime, the cavity mode is
adiabatically eliminated generating an effective model for the qubits alone.
The characteristic long-range order of the Lipkin-Meshkov-Glick model is here
mediated by the cavity field. For a closed qubit system, the inherent second
order phase transition of the qubits is reflected in the intensity of the
output cavity field. In the broken symmetry phase, the many-body ground state
is highly entangled. Relaxation of the qubits is analyzed within a mean-field
treatment. The second order phase transition is lost, while new bistable
regimes occur.
