Possible breakdown of the Alexander-Orbach rule at low dimensionalities

Amnon Aharony*, D. Stauffer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2368-2370
Number of pages3
JournalPhysical Review Letters
Issue number26
StatePublished - 1984


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