Let us describe this equivalence in the 2 dimensional case.

Notice how this resembles the expression from the finite dimensional case.

For 1 dimensional case, we can guess that the screening effects only on the field lines which are very close to the wire axis.

We'll focus on the one dimensional case, the proof in higher dimensions is similar.

Just as in the one dimensional case, we will shift attention from the spins to the spin-flips.

In the finite dimensional case, there is a somewhat more explicit formulation.

Note that this is in sharp contrast with the finite dimensional case.

This algorithm is also applicable to the three dimensional case.

In the one dimensional case, the support of is the interval .

In the (1 + 1)-dimensional case the commutation rules between and are particularly simple.