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Field-theoretic approach to biconnectedness in percolating systems
A general method is given whereby $m$-connectedness correlation functions can be studied in the percolation problem. The method for $m=1$ involves calculating the kth power of the correlation function $ 〈\ensuremath{\sigma}(x)\ensuremath{\sigma}({x}^{\ensuremath{'}})〉 $ for a randomly dilute Ising model at nonzero temperature and subsequently averaging over configurations. The final step is …