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 non-trivial 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.

4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communication

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• Aperiodic Ising Quantum Chains
• Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
• Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model
• Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
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