Monte Carlo Renormalization of the Three-Dimensional Ising Model: The Influence of Truncation

Abstract

We have applied the Monte Carlo renormalization technique to the simple cubic Ising model. In particular we have investigated the influence of truncation, i.e. the number of coupling used in the analysis of the conjugate correlation functions generated by the Monte Carlo and spin blocking algorithms. To this purpose we have included up to 36 even and 21 odd couplings in our analysis, which is considerably more than used so far. We find that the addition of extra couplings does significantly influence the largest eigenvalues of the stability matrices. However, after correction for the finite-size effect and extrapolation to the fixed point, the effects on the estimated critical exponents are no longer significant.