One-dimensional percolation problems with further neighbour bonds-transfer-matrix approach

The transfer-matrix method is used to find the exact expressions for the correlation length in the critical region for both one-dimensional site and bond percolation problems with bonds connecting Lth-nearest neighbours (for any finite L). For the site percolation, the correlation length exponent v is found to be L, consistent with the result obtained from the generating function method. For the bond percolation, we find v=L(L+1)/2.