TY - JOUR
T1 - Possible breakdown of the Alexander-Orbach rule at low dimensionalities
AU - Aharony, Amnon
AU - Stauffer, D.
PY - 1984
Y1 - 1984
N2 - Simple conditions are presented under which the fractal dimension of a random walk on an aggregate, dw, is given by dw=D+1, where D is the aggregate's fractal dimension. These conditions are argued (with one simple speculative assumption) to apply for D<2, implying a breakdown of the Alexander-Orbach rule dw=3D2. Existing results for percolation clusters, lattice animals, and diffusion-limited aggregates seem to favor our new rule.
AB - Simple conditions are presented under which the fractal dimension of a random walk on an aggregate, dw, is given by dw=D+1, where D is the aggregate's fractal dimension. These conditions are argued (with one simple speculative assumption) to apply for D<2, implying a breakdown of the Alexander-Orbach rule dw=3D2. Existing results for percolation clusters, lattice animals, and diffusion-limited aggregates seem to favor our new rule.
UR - https://www.scopus.com/pages/publications/4243572031
U2 - 10.1103/PhysRevLett.52.2368
DO - 10.1103/PhysRevLett.52.2368
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AN - SCOPUS:4243572031
SN - 0031-9007
VL - 52
SP - 2368
EP - 2370
JO - Physical Review Letters
JF - Physical Review Letters
IS - 26
ER -