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Genuine Multipartite Entanglement in the $XY$ Model

We analyze the $XY$ model characterized by an anisotropy $γ$ in an external magnetic field $h$ with respect to its genuine multipartite entanglement content (in the thermodynamic and finite size case). Despite its simplicity we show that the quantity -detecting genuine multipartite entanglement through permutation operators and being a lower bound on measures- witnesses the presence of genuine multipartite entanglement for nearly all values of $γ$ and $h$. We further show that the phase transition and scaling properties are fully characterized by this multipartite quantity. Consequently, we provide a useful toolbox for other condensed matter systems, where bipartite entanglement measures are known to fail.