  We formalize and extend an operational multipartite entanglement measure
introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A
73, 010305(R) (2006), through the generalization of global entanglement (GE)
[D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to
GE the main feature of this measure lies in the fact that we study the mean
linear entropy of all possible partitions of a multipartite system. This allows
the construction of an operational multipartite entanglement measure which is
able to distinguish among different multipartite entangled states that GE
failed to discriminate. Furthermore, it is also maximum at the critical point
of the Ising chain in a transverse magnetic field, being thus able to detect a
quantum phase transition.
