SERIES EXPANSION ANALYSIS OF THE BACKBONE PROPERTIES OF 2-DIMENSIONALPERCOLATION CLUSTERS

Low-density series expansions for the backbone properties of two-dimen sional bond percolation clusters are derived and analysed. Expansions for most of the 14 properties considered are new and are obtained to o rder p(18) on the square lattice and order p(14) on the triangular lat tice. Earlier series work was confined to three properties of the squa re lattice and was to order p(10). The fractal dimension of the bonds or sites in the backbone is estimated to be D-B = 1.605 +/- 0.015 and is intermediate between a previously conjectured field theory value an d the latest Monte Carlo results, The union, intersection and length o f the longest self-avoiding paths are found to have the same fractal d imension which is close to D-B and consistent with the field theory co njecture for D-B. On the other hand, the union intersection and length of the shortest paths are found to have different dimensions and in t he case of the intersection, the triangular and square lattices are fo und to have significantly different dimensions. The fractal dimension of the shortest path also appears to be non-universal and we find d(mi n) = 1.106 +/- 0.007 for the square lattice and 1.148 +/- 0.007 for th e triangular lattice. Critical amplitude ratios are considered and fou nd to be in agreement with theoretical inequalities.