MONTE-CARLO RENORMALIZATION-GROUP STUDY OF THE 3-DIMENSIONAL ISING-MODEL

We present results of a Monte Carlo renormalization-group study of the three-dimensional Ising model on 64(3) and 128(3) simple-cubic lattices. The eigenvalues of a linearized transformation matrix, constructed with the use of 53 even operators and 46 odd operators, are shown to be free of truncation errors. Our estimate of the critical coupling is 0.221 652 +/- 0.000 003 +/- 0.000 001 where the first error is statistical and the second due to the finite number of blocking steps. The results for the relevant exponents are nu = 0.624(2) and eta = 0.026(3). This estimate for nu lies 2-3-sigma below that obtained from other methods. The correction-to-scaling exponent is found to lie in the range omega = 0.8-0.85. We also find that the subleading magnetic exponent is relevant and present evidence that it corresponds to a redundant eigenvector of the majority-rule blocking transformation.