The Topological Nonconnectivity Threshold and magnetic phase transitions in classical anisotropic long-range interacting spin systems

We review, with emphasis on the dynamical point of view, the classical characteristics of the Topological Nonconnectivity Threshold (TNT), recently introduced in F. Borgonovi, G.L. Celardo, M. Maianti and E. Pedersoli, J. Stat. Phys. <Emphasis Type="Bold">116, 1435 (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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006