  We derive a general relation between the non-analyticities of the ground
state energy and those of a subclass of the multipartite generalized global
entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A
73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both
a critical point location and the order of a quantum phase transition (QPT). We
also show that GGE allows us to study the relation between multipartite
entanglement and QPTs, suggesting that multipartite but not bipartite
entanglement is favored at the critical point. Finally, using GGE we were able,
at a second order QPT, to define a diverging entanglement length (EL) in terms
of the usual correlation length. We exemplify this with the XY spin-1/2 chain
and show that the EL is half the correlation length.
