Longest path in percolating hierarchical lattice

We determine numerically the probability distribution for the longest self-avoiding path lengths connecting two distant points on a diluted hierarchical lattice at the percolation threshold. The evolution of this distribution with the system size is studied and the distribution is observed to approach a universal scale-invariant form under proper rescaling of its argument. The longest path length scales as |p^max| and our estimate for _max=1.816±0.013 is clearly different from the previously estimated _min=1.531+0.002 for the shortest path lengths on the same hierarchical lattice. This gives support to the multifractal behavior of SAWs on percolating clusters.