Power-law corrections to exponential decay of connectivities and correlations in lattice models
Power-law corrections to exponential decay of connectivities and correlations in lattice models
Consider a translation-invariant bond percolation model on the integer lattice which has exponential decay of connectivities, that is, the probability of a connection $0 \leftrightarrow x$ by a path of open bonds decreases like $\exp\{-m(\theta)|x|\}$ for some positive constant $m(\theta)$ which may depend on the direction $\theta = x/|x|$. In …