We rigorously prove that the probability Pn that the origin of a d-dimensional lattice belongs to a cluster of exactly n sites satisfies Pn > exp(-αn(d-1)/d) whenever percolation occurs. This holds for the usual (noninteracting) percolation models for any concentration p > pc, as well as for the equilibrium states of lattice spin systems with quite general interactions. Such a lower bound applies also if no percolation occurs, but if it appears in some other phase of the system.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics