Finite size effects and pseudocritical behavior .1. Ising spin and lattice gauge models

We deal with the transfer matrices built by Kramers and Wannier's successive screw method for 2-d (l x infinity l less than or equal to 27) and 3-d (l x m x infinity, lm less than or equal to 27) Ising spin systems and 3-d (I x m x infinity, lm less than or equal to 9) Ising lattice gauge systems, and examine to what extent the presently available supercomputers can improve our previous results on the pseudocritical properties of the systems. Using the shift exponent relation for the pseudocritical parameters obtained from the specific heat anomaly, we estimate the bulk values K-c. We considerably improve our previous results, but the precision for the 3-d spin system falls behind that of the latest Monte Carlo result. We also evaluate K-c in two dimensions from the correlation length anomaly in agreement with the exact value to eight decimal places. We efficiently extrapolate the quantities of the 3-d lattice by the consecutive difference procedure. We propose the inflection point method in order to extract the critical indices from the anomaly curve families.