Universality classes of Ising systems with long-range interactions on Sierpiński-gasket-like lattices

Universality criteria for Ising systems with two-point long-range interactions on Sierpiński-gasket-like lattices of many length parameters are established. The long-range interactions are introduced in a self-similar way, reflecting the fractal structure of the lattices. The systems are shown to be uniquely classified according to universality by two quantities: the fractal dimension and the so-called critical dimension, which characterizes some topological properties of the lattices and long-range properties of the systems at critical points.