  Understanding the electronic properties of quasicrystals, in particular the
dependence of these properties on dimension, is among the interesting open
problems in the field of quasicrystals. We investigate an off-diagonal
tight-binding Hamiltonian on the separable square and cubic Fibonacci
quasicrystals. We use the well-studied singular-continuous energy spectrum of
the 1-dimensional Fibonacci quasicrystal to obtain exact results regarding the
transitions between different spectral behaviors of the square and cubic
quasicrystals. We use analytical results for the addition of 1d spectra to
obtain bounds on the range in which the higher-dimensional spectra contain an
absolutely continuous component. We also perform a direct numerical study of
the spectra, obtaining good results for the square Fibonacci quasicrystal, and
rough estimates for the cubic Fibonacci quasicrystal.
