The SW algorithm does however satisfy detailed-balance. To show this, we note that every transition between two Ising spin states must pass through some bond configuration in the percolation representation. Let's fix a particular bond configuration: what matters in comparing the probabilities related to it is the number of factors q = e − − 2 β β J for each missing bond between neighboring spins with the same value; the probability of going to a certain Ising configuration compatible with a given bond configuration is uniform (say p ). So the ratio of the transition probabilities of going from one state to another is