Fracton Excitations in the Magnetic "Net Fractal" Systems

Abstract

A localized spin system of fractal symmetry and Heisenberg exchange between nearest neighbors is considered. We define a specific class of fractals: "net fractals" and prove that in the logarithmic scale they are isomorphic with some bulk crystals. Further, with the use of logarithmic coordinates we show that the "net fractal" magnetic fractons can be presented as the conventional magnons.