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.