The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions, from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.
International Journal of Modern Physics C
- Pub Date:
- Universal scaling functions;
- Boundary conditions;
- Multiple scanning clusters;
- Condensed Matter - Statistical Mechanics
- 8 pages, latex, 4 eps figures included, to appear in Int. Journal of Modern Physics C