Exact solution of the one-dimensional percolation problem with further neighbour bonds

Abstract

The authors obtain an exact solution for the one-dimensional site percolation model with bonds connecting the Lth nearest neighbours. The critical exponents are found to depend on L:2- alpha _p=L, gamma _p=L, nu _p=L, eta ₀=1, beta _p=0 and delta _p= infinity . By mapping the percolation problem onto an Ising-like model with multi-spin interactions, it is argued that the dependence of the percolation exponents on L can be understood from consideration of Ising model universality classes.