Entanglement and symmetry effects in the transition to the Schroedinger cat regime

We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superposition content exponentially with the size $N$, a decrease of the order of 1/N is observed when the XXX model is considered. The emergence of two qualitatively different regimes is directly related to the difference in the symmetry of the models.