A Ferromagnetic Lieb-Mattis Theorem
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Publication:6469222
DOI10.1103/PHYSREVLETT.94.057206arXivmath-ph/0408020WikidataQ81559256 ScholiaQ81559256MaRDI QIDQ6469222
Shannon Starr, Bruno Nachtergaele
Publication date: 11 August 2004
Abstract: We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains of any spin and XXZ spin chains with all spins equal to 1/2. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.
Quantum equilibrium statistical mechanics (general) (82B10) Statistical mechanics of magnetic materials (82D40)
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