Possible Tests and Improvements for Monte Carlo Renormalization-Group Studies

Exploiting the solvability of the $d=2\mathrm{}$ 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 $d=3\mathrm{}$.