Analogously, for the cluster in b, also the construction came to a halt

because none of the possible minus-minus edges accross the boundaries were accepted.

There are 18 minus-minus edges in b, so the a-priori probability from b to a

is proportional to (1-p)^18.

Now, let us consider the statistical weights of configurations a and b:

again, there are terms outside the cluster, but they are the same in a and b.

There are terms inside the cluster, also they are the same in a and b. The game is played at the boundary.

Now, in configuration a, threy are 18 terms plus-minus, hence 18 terms +1

and 14 terms -1 in the energy,

or if we write N1 instead of +1 and N2 instead of the terms plus-plus,

the energy accross the boundary is N1-N2 in a,

and it is N2-N1 in b.

Now, we have all that it takes to write down the detailed balance condition,

like here, we have the statistical weight of configuration a, times the a-priori probability to construct this cluster

times the acceptance probability to move from a to be,

equals the statistical weight times the construction probability times the acceptance probability from be to a.

This gives the Metropolis acceptance rate shown here,