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Statistical mechanics of the Cluster-Ising model

By Pietro Smacchia, Luigi Amico, Paolo Facchi, Rosario Fazio, Giuseppe Florio, Saverio Pascazio and Vlatko Vedral


We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Neverthless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.Comment: To be published in Physical Review

Topics: Quantum Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory
Year: 2011
DOI identifier: 10.1103/PhysRevA.84.022304
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