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First-order transitions for some generalized \(XY\) models. (English) Zbl 1122.82013

Summary: We demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized \(XY\) models, and also point out the connection between them and annealed site-diluted (lattice-gas) continuous-spin models.

MSC:

82B26 Phase transitions (general) in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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