  We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG)
model with nitrogen-vacancy (NV) center ensembles in diamond magnetically
coupled to superconducting coplanar waveguide cavities. With the assistance of
external microwave driving fields, we show that the interaction of the NV spins
can be easily controlled, and several types of the LMG model can be realized by
tuning the different parameters. Under the thermal dynamical limit, the
distinct non-equilibrium second order quantum phase transition of the spin
ensemble can be achieved at the critical point. Furthermore, we show that the
spin squeezed state can be generated by tailoring the LMG Hamiltonian to
possess the two-axis counter-twisting form in this hybrid quantum system.
