A method is discussed to analyze multifractal properties of spectra and wave functions by means of an entropy function. The method is exemplified on a model for lattice vibrations in an incommensurate crystal phase. It is shown that the model has a spectrum with scaling properties. Moreover, it is probably singular continuous, which is a rather exceptional case. This is even true when the spectrum becomes a fat fractal. The scaling properties of the mode wave functions are discussed.

• Received 11 December 1987

DOI:https://doi.org/10.1103/PhysRevB.38.5811