Swendsen-Wang (SW) found that by placing bonds between neighboring sites with the same spin value, the Potts model can be written in terms of interacting clusters of connected spins.
For the particular choice 
(
)
the interaction energy is zero, so the clusters are independent. This means
we can update all the clusters (by changing the current spin values to a
random new spin value) completely independently.
Since the clusters can be very large, the update is highly non-local, and z can be very small (even zero).