Genuine Tripartite Entanglement in a Spin-Star Network at Thermal Equilibrium

In a recent paper [M. Huber {\it et al}, Phys. Rev. Lett. {\bf 104}, 210501 (2010)] new criteria to find out the presence of multipartite entanglement have been given. We exploit these tools in order to study thermal entanglement in a spin-star network made of three peripheral spins interacting with a central one. Genuine tripartite entanglement is found in a wide range of the relevant parameters. A comparison between predictions based on the new criteria and on the tripartite negativity is also given.
Comment: 8 pages, 13 figures