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

The alpha -XY model generalizes, through the introduction of a power-law de caying potential, a well-studied mean-field Hamiltonian model with attracti ve long-range interactions. In the alpha -model, the interaction between cl assical rotators on a lattice is gauged by the exponent alpha in the coupli ngs decaying as r(z), where r are distances between sites, We review and co mment here a few recent results on the static and dynamic properties of the alpha -model. We discuss the appropriate alpha -dependent rescalings that map the canonical thermodynamics of the alpha -model into that of the mean- field model. We also show that the chaotic properties of the model, studied as a function of a display a universal behaviour. (C) 2001 Elsevier Scienc e Ltd. All rights reserved.