Nonextensive scaling in a long-range Hamiltonian system

The nonextensivity of a classical long-range Hamiltonian system is discussed. The system is the so-called alpha-XY model, a lattice of inertial rotators with an adjustable parameter alpha controlling the range of the interactions. This model has been explored in detail over the last years. For sufficiently long-range interactions, namely alpha < d, where d is the lattice dimension, it was shown to be nonextensive and to exhibit a second-order phase transition. However, conclusions in apparent contradiction with the findings above have also been drawn. This picture reveals the fact that there are aspects of the model that remain poorly understood. Here we perform a thorough analysis, essaying to understand the origin of the apparent discrepancies. (C) 2004 Elsevier B.V. All rights reserved.