Hyperscaling and crossover exponents near the percolation threshold

Y. Gefen*, A. Aharony, Y. Shapir, A. Nihat Berker

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The critical exponents which describe quantities which are measured per unit 'mass' of the infinite cluster near percolation are shown to be shifted by beta p (the exponent describing the probability of belonging to this cluster). The fractal dimensionality of the infinite cluster then replaces the Euclidean one in hyperscaling relations. The crossover exponent for the effects of random fields on dilute Ising models are zero temperature is then shown to be phi h= gamma p+ beta p. Similarly, that for random local concentrations is phi p= alpha p+ beta p.

Original languageEnglish
Article number001
Pages (from-to)L801-L805
JournalJournal of Physics C: Solid State Physics
Issue number24
StatePublished - 1982


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