Dealing with truncation in monte carlo renormalization-group calculations

We use the d=2 Ising model as a concrete example to show that truncation of the derivative matrix T to a subspace S of short-range interactions needs some justification, since each row of T contains arbitrarily large elements in the long-range sector. We point out that despite this a small parameter justifying truncation may exist, we show how to find it, and we perturbatively correct the errors due to truncation, all without leaving S. The bulk of our analysis carries over to other Monte Carlo renormalization-group studies, particularly the d=3 Ising model.