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

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 a universal behaviour.