Possible tests and improvements for Monte Carlo renormalization-group studies

Exploiting the solvability of the d=2 nearest-neighbor Ising model we construct the critical surface in a thirteen-dimensional parameter space in the vicinity of the nearest-neighbor transition point. We see if the flows generated from this point by recent Monte Carlo renormalization-group transformations lie on this surface. We clarify and quantify the effects of truncation. We unearth a truncation scheme that should speed up the convergence to the fixed point even in d=3.