Interface Fluctuations on a Hierarchical Lattice
arXiv:cond-mat/9606057 · doi:10.1103/PhysRevE.54.1106
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.
14 pages plain Tex, one Figure upon request, Phys Rev E (in print)
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