Higher connectivity in random mixtures = the universality class of 2-cluster percolation

Higher connectivity percolation (site valence ⩾ 2) is considered for selected 2, 3, 4-dimensional lattices, by the method of exact series expansions. The set of critical exponents obtained from the perimeter-to-size ratio and the moments of the cluster size distribution favours the same universality class as for normal percolation. The animal statistics are found to be unaffected by the connectivity requirement and an “effective volume” influence is detected in the critical region for 2-dimensional lattices.