Percolation transition of strongly connected clusters in finite dimensions and on complete graphs (opens in new tab)

We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to $7$ and complete graphs. Below the upper critical dimension $d_u=6$, the critical SCCs exhibit nontrivial fractal dimension $d_{\rm SCC}$, and the size distribution scales as $\sim s^{-\tau_{\rm SCC}}$ with the ...