and a cluster is formed by randomly selecting a site and percolating through the adjacent sites with q = − − 1 (with a percolation ratio of 1) until the maximal cluster is formed. The spins in the cluster are then exchanged between the two replicas. It can be shown that the exchange update is isoenergetic, meaning that the total energy is conserved in the update. This gives an acceptance ratio of 1 as calculated from the Metropolis-Hastings rule. In other words, the update is rejection-free.