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

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.