The efficiency of this algorithm is highly sensitive to the site percolation threshold of the underlying lattice. If the percolation threshold is too small, then a giant cluster will likely span the entire lattice, resulting in the trivial update of exchanging nearly all the spins between the replicas. This is why the original algorithm only performs well in low dimensional settings (where the site percolation ratio is sufficiently high). To efficiently extend this algorithm to higher dimensions, one has to perform certain algorithmic interventions.