  We investigate quantum phase transitions in various spin chain systems using
the multipartite entanglement measure $\tau_{SEF}$ based on the monogamy
inequality of squared entanglement of formation. Our results demonstrate that
$\tau_{SEF}$ is more effective and reliable than bipartite entanglement or
bipartite correlation measures such as entanglement of formation, von Neumann
entropy, and quantum discord in characterizing quantum phase transitions.
$\tau_{SEF}$ not only detects critical points that may go unnoticed by other
detectors but also avoids the issue of singularity at non-critical points
encountered by other measures. Furthermore, by applying $\tau_{SEF}$, we have
obtained the phase diagram for the XY spin chain with three and four
interactions and discovered a new quantum phase.
