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• W2065660519 abstract "Abstract The simplest plane rotator model consists of two-component unit vectors, associated with a D-dimensional lattice (say Z D ), parameterized by polar angles ϕj, and interacting via a ferromagnetic potential restricted to nearest neighbours U=Ujk=−ϵcos(ϕj−ϕk); here ϵ is a positive quantity setting energy and temperature scales (i.e., T ∗ =k B T/ϵ ). On the other hand, the xy model involves three-component unit vectors, parameterized by polar angles (θk,φk), but with two components only coupled by the interaction, i.e., V=Vjk=−ϵsinθjsinθkcos(φj−φk). We consider here generalized xy models, where the interaction is defined by W=Wjk=−ϵ(sinθjsinθk)Lcos(φj−φk), L∈ N , L⩾1, and point out rigorous comparison inequalities holding for them; in turn, these can be used to prove existence and type of phase transitions when D⩾2; Mean Field and Two-Site Cluster estimates of the ordering transition temperatures are calculated as well, for D=3 and L⩽4." @default.
• W2065660519 created "2016-06-24" @default.
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• W2065660519 date "2002-09-01" @default.
• W2065660519 modified "2023-09-25" @default.
• W2065660519 title "On the xy model and its generalizations" @default.
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• W2065660519 doi "https://doi.org/10.1016/s0375-9601(02)01077-0" @default.
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