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Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations

Tsuneyoshi Nakayama, Kousuke Yakubo, and Raymond L. Orbach

Tsuneyoshi Nakayama and Kousuke Yakubo

  • Department of Applied Physics, Hokkaido University, Sapporo 060, Japan

Raymond L. Orbach

  • Department of Physics, University of California, Riverside, California 92521

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Rev. Mod. Phys. 66, 381 – Published 1 April, 1994

DOI: https://doi.org/10.1103/RevModPhys.66.381

Abstract

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.

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Rev. Mod. Phys. 66, 381– Published 1 April, 1994

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