T. Nakayama et al., DYNAMICAL PROPERTIES OF FRACTAL NETWORKS - SCALING, NUMERICAL SIMULATIONS, AND PHYSICAL REALIZATIONS, Reviews of modern physics, 66(2), 1994, pp. 381-443
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 li
mited to a specific structure, the percolating network. Recent progres
s has followed three directions: scaling, numerical simulations, and e
xperiment. In a happy coincidence, large-scale computations, especiall
y those involving array processors, have become possible in recent yea
rs. Experimental techniques such as light- and neutron-scattering expe
riments have also been developed. Together, they form the basis for a
review article useful as a guide to understanding these developments a
nd for charting future research directions. In addition, new numerical
simulation results for the dynamical properties of diluted antiferrom
agnets are presented and interpreted in terms of scaling arguments. Th
e authors hope this article will bring the major advances and future i
ssues facing this field into clearer focus, and will stimulate further
research on the dynamical properties of random systems.