Critical behavior of the Gaussian model on a diamond-type hierarchical lattice with periodic and aperiodic interactions

The critical behavior of the Gaussian models on a diamond-type hierarchical lattice with periodic and aperiodic interactions according to a class of substitution sequences are studied by the exact renormalization-group approach and spin rescaling. For the periodic case with a two-letter general Fibonacci sequence given by the generating substitutions A→AB, B→AB and the aperiodic case with the generating substitutions A→AB, B→BA, the critical behaviors are found unchanged with respect to the uniform case and belong to the same universality of the uniform case. For the other aperiodic case with the generating substitutions A→AB, B→AA, the geometric fluctuation is relevant by Luckʹs criterion and the critical phenomena of the uniform and periodic cases are found to disappear.