ABSTRACT
The magnetic excitations spectra of a system are linked to the existence of spin waves. The modulation of the amplitudes of magnetic excitations exhibits a complex structure; new geometry superposed on the underlying fractal network appears, underlined by nodal curves where the amplitude is very low. In this chapter, the authors describe the two main categories of Sierpinski fractals they have to distinguish, namely the deterministic and random ones. The whole set of results of canonical Monte Carlo simulations supports the occurrence of a second-order phase transition of the Ising model on deterministic Sierpinski fractals provided that the ramification order is infinite. Besides the trivial monodimensional case, a complete analytical solution of the statistical problem linked to the Ising model is hitherto available only in the bidimensional case. Sierpinski carpets and their generalization to higher dimensions by Menger provide a generic model of fractals that has been widely used to model physical phenomena in non-integer dimensions.
