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 $q).\mathrm{}$ The critical exponents do not depend on the strengths of the exchange interactions.

• Received 30 June 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3330