Strong-disorder renormalization-group method on fractal lattices: Heisenberg models and magnetoresistive effects in tight-binding models

We use a numerical implementation of the strong disorder renormalization group (RG) method to study the low-energy fixed points of random Heisenberg and tight-binding models on different fractal lattices. For the Heisenberg model types of infinite disorder and strong disorder fixed points are found. For the tight-binding model we add an orbital magnetic field and use both diagonal and off-diagonal disorder. For this model, in addition to the gap spectra, we also study the fraction of frozen sites, the correlation function, the persistent current, and the two-terminal current. The lattices with an even number of sites around each elementary plaquette show a dominant ${\ensuremath{\phi}}_{0}=h∕e$ periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant ${\ensuremath{\phi}}_{0}∕2$ periodicity at vanishing diagonal disorder, with a positive weak localizationlike magnetoconductance at infinite disorder fixed points. The magnetoconductance with both diagonal and off-diagonal disorder depends on the symmetry of the distribution of on-site energies.