Abstract
A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size . This number should become independent of for dimensions and vary as at . The predictions for depend on the boundary conditions, and the results there may vary between and . While simulations in six dimensions are consistent with this prediction [after including corrections of order ], in five dimensions the average number of spanning clusters still increases as even up to . However, the histogram of the spanning cluster multiplicity does scale as a function of , with , indicating that for sufficiently large the average will approach a finite value: a fit of the five-dimensional multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for and for are also presented.
4 More- Received 11 July 2004
DOI:https://doi.org/10.1103/PhysRevE.70.056116
©2004 American Physical Society