Universal critical behavior of aperiodic ferromagnetic models

Abstract

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of q-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a nontrivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle, which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent alpha of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of q). The critical exponents do not depend on the strengths of the exchange interactions.