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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.