Renormalization Group in coordinate space

We now want to see how we can build the RG transformation from the coarse graining procedure. We will first use two different decimation techniques for a one-dimensional Ising model, and then see what happens for . As we have partially anticipated, we will see that as soon as we will no longer work in the "easy" case things will get really complicated because at every iteration of the RG new interactions appear, and so the problem becomes rapidly impossible to handle; we will therefore be forced to resort to approximations.