We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both s...

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, form self-similar, fractal geometric clusters. this paper, we advance theory criticality as it pertains to those clusters (defined connected sets nearest-neighbor aligned spins) in context Ising models. We show how data from can be used distinguish whether electronic observed a...