  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.
