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In this paper we consider the quantum phase transition in the Ising model inthe presence of a transverse field in one, two and three dimensions from amulti-partite entanglement point of view. Using \emph{exact} numericalsolutions, we are able to study such systems up to 25 qubits. The Meyer-Wallachmeasure of global entanglement is used to study the critical behavior of thismodel. The transition we consider is between a symmetric GHZ-like state to aparamagnetic product-state. We find that global entanglement serves as a goodindicator of quantum phase transition with interesting scaling behavior. We usefinite-size scaling to extract the critical point as well as some criticalexponents for the one and two dimensional models. Our results indicate thatsuch multi-partite measure of global entanglement shows universal featuresregardless of dimension $d$. Our results also provides evidence thatmulti-partite entanglement is better suited for the study of quantum phasetransitions than the much studied bi-partite measures.

Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model