Critical properties of Ising models with long-range interactions on Sierpiński-gasket lattices in higher Euclidean dimensions

Abstract

Ising systems with two-spin long-range interactions are studied on Sierpiński-gasket lattices generalized to Euclidean dimensions d = 3, 4, 5, 6. For each lattice, the long-range interactions are assigned to edges that are part of the appropriate self-similar structure. In consequence, these systems are infinitely ramified, and exhibit critical behavior at finite temperatures. An analysis of critical properties of the systems, in particular the calculation of critical exponents, is carried out by using an exact renormalization-group method. It is shown that there exists some similarity between critical properties of the long-range interacting fractal models under study here and critical properties of short-range interacting Ising models defined on abstract regular lattices interpolated to noninteger dimensionalities.