In this expanded version of an earlier letter, we consider many computational
details that were omitted for want of space. For d= 2 Ising spins with up to 13
different short-range interactions, we construct the critical surface in the vicinity
of (Onsager's) nearest-neighbor (nn) critical point by using the body of the
available information on the solvable nn case. We then see if the Monte Carlo
renormalization group flows generated from this point do indeed lie on this sur-
face and quantify the errors if they do not