Spin models and cluster distributions for bond and site percolation models

The bond and site percolation models are formulated as the limit of spin models and spin Hamiltonians are obtained for these models. The order parameters in each case provide generating functions for the site and bond distributions in the clusters. The form of the site-bond distribution is discussed and shown to be extremely narrow near $p_c$. Critical exponents are obtained near one dimension and shown to be the same for the two models.