Multifractal properties of aperiodic Ising models with competition and frustration

The role of competition and frustration on the multifractal properties of the local magnetization of aperiodic Ising models defined on hierarchical lattices is analyzed. Competing ferro-antiferromagnetic interactions are introduced by a deterministic two-letter aperiodic sequence, while frustration is induced by appropriated choice of boundary conditions. Two models are investigated, where the coupling constant distributions lead to relevant (irrelevant) geometrical fluctuations that alter (not alter) the critical properties of the system, with respect to those of the homogeneous one. The profiles of the local magnetization are calculated by an exact procedure as a function of the temperature. Multifractal analysis is performed indicating that the F(α)-spectrum does not survive below the critical temperature (Tc) for the irrelevant model when non-frustrated boundary conditions are considered. For relevant fluctuations, however, the spectra survive below Tc when both non-frustrated and frustrated boundary conditions are considered.