Berezinskii-Kosterlitz-Thouless-type Transition in Site Percolation on the Diamond Hierarchical Lattice (opens in new tab)

We study site percolation on the diamond hierarchical lattice, a finite-dimensional fractal network, using an exact generating-function analysis. In contrast to bond percolation, site percolation on this lattice does not undergo a transition from a nonpercolating phase to a percolating phase. Instead, the system exhibits a nonpercolating phase for $pp_{\rm c}$. In the critical phase, the size of the largest cluster remains subextensive, scaling ...