J. Physique Lett. 45, 401-407 (1984)
DOI: 10.1051/jphyslet:01984004509040100

Fluctuations of the mass of the infinite cluster at percolation

A. Kapitulnik, N. Frid et G. Deutscher

Department of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel

Abstract
We have measured the fluctuations of the mass M of the infinite cluster in percolation, as well as those of fractal objects and discontinuous thin films of Pb. It was found that these fluctuations diverge with the length scale with an exponent equal to twice the fractal dimensionality. A scaling argument is given to explain that result.

Résumé
Nous avons mesuré les fluctuations de la masse M d'un amas infini de percolation, ainsi que celles d'objets fractals et de couches minces discontinues de Pb. On trouve que ces fluctuations divergent en fonction de l'échelle de longueur avec un exposant égal au double de la dimension fractale. Ce résultat est expliqué par un argument de loi d'échelle.

PACS
0550 - Lattice theory and statistics: Ising problems.
7150 - Localized single particle electronic states.
7360D - Electrical properties of metals and metallic alloys thin films/low dimensional structures.

Key words
discontinuous metallic thin films -- electrical conductivity of solids -- electronic conduction in metallic thin films -- fluctuations -- lead -- localised electron states -- percolation -- mass fluctuations -- infinite cluster -- percolation -- fractal objects -- discontinuous thin films -- Pb -- length scale -- fractal dimensionality -- scaling argument