Density of states and magnetic susceptibilities on the octagonal tiling

We study electronic properties as a function of the six types of local environments of the octagonal quasiperiodic tiling using a tight-binding model. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two sites are equivalent in a quasiperiodic tiling. We present the site-dependent magnetic susceptibility of electrons on this tiling, which also has six characteristic dependences on energy. We show the existence of a non-local spin susceptibility, which decays with the square of the distance between sites and corresponds to quasiperiodic Ruderman-Kittel oscillations. We investigate the formation of local magnetic moments when electron-electron interactions are included