The Topological Non-connectivity Threshold and magnetic phase transitions in classical anisotropic long-range interacting spin system

We analyze from the dynamical point of view the classical characteristics of the Topological Non-connectivity Threshold (TNT), recently introduced in F.Borgonovi, G.L.Celardo, M.Maianti, E.Pedersoli, J.Stat.Phys.,116,516(2004). This shows interesting connections among Topology, Dynamics, and Thermo-Statistics of ferro/paramagnetic phase transition in classical spin systems, due to the combined effect of anisotropy and long-range interactions.