Universal behavior in the static and dynamic properties of the α-XY model

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The α-XY model generalizes, through the introduction of a power-law decaying potential, a well studied mean-field hamiltonian model with attractive long-range interactions. In the α-model, the interaction between classical rotators on a lattice is gauged by the exponent α in the couplings decaying as rα, where r are distances between sites. We review and comment here a few recent results on the static and dynamic properties of the α-model. We discuss the appropriate α dependent rescalings that map the canonical thermodynamics of the α-model into that of the mean field model. We also show that the chaotic properties of the model, studied as a function of α display an universal behaviour.