# Renormalization Group in coordinate space

We now want to see how we can build the RG transformation ${\displaystyle R_{\ell }}$ 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 ${\displaystyle d=2}$. As we have partially anticipated, we will see that as soon as we will no longer work in the "easy" case ${\displaystyle d=1}$ 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.