Infinite set of exponents describing physics on fractal networks

R. Blumenfeld*, Y. Meir, A. B. Harris, A. Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The generalised resistance between connected points a distance L apart on fractal networks of nonlinear (V approximately Ialpha) resistors scales as Lzeta (/alpha ). It is shown that zeta ( alpha ) for alpha =- infinity , -1, 0-, 0+, 1 and infinity , describes physically relevant geometrical properties and d zeta /d alpha <or=0. For percolating clusters approximants are given for zeta for - infinity < alpha < infinity in 2-6 dimensions. For alpha <0 a family of solutions to Kirchhoff's equations exists, reminiscent of metastable states in spin glasses.

Original languageEnglish
Article number007
Pages (from-to)L791-L796
JournalJournal of Physics A: Mathematical and General
Volume19
Issue number13
DOIs
StatePublished - 1986

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