Interface Fluctuations on a Hierarchical Lattice

TL;DR

This paper investigates interface fluctuations on a hierarchical lattice, revealing anomalous behavior and discontinuous fluctuation exponents through analytical methods, linking classical interface problems with quantum diffusion in hierarchical potentials.

Contribution

It provides the first analytical calculation of interface fluctuation exponents on a hierarchical lattice, demonstrating their discontinuity at the homogeneous limit.

Findings

Interface fluctuation exponents are discontinuous at the homogeneous lattice limit.

Hierarchical perturbations are relevant according to a modified Harris criterion.

Analytical results obtained via transfer-matrix and renormalization group techniques.

Abstract

We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional hierarchical potential. According to a modified Harris criterion this type of perturbation is relevant and one expects anomalous fluctuating behavior. By transfer-matrix techniques and by an exact renormalization group transformation we have obtained analytical results for the interface fluctuation exponents, which are discontinuous at the homogeneous lattice limit.