Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond-Type Hierarchical Lattices in External Magnetic Fields**The project supported by the National Basic Research Project “Nonlinear Science”, National Natural Science Foundation of China, the Zhejiang Provincial “151 Talent Engineering” Foundation and the Wenzhou Municipal “551 Talent Engineering” Foundation of China

Abstract

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.