Entanglement in a second order quantum phase transition

We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point $lambda_c$, in the thermodynamic limit. We also show that there exists a value $lambda_0 geq lambda_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.