Monte Carlo renormalization of the three-dimensional Ising model

Abstract We have investigated the simple cubic Ising model by means of the Monte Carlo renormalization technique. The emphasis of our study concerns the influence of truncation, i.e. the dimensionality of the coupling subspace in which the analysis of the correlation functions generated by the Monte Carlo and spin blocking algorithms is performed. To this purpose we have included up to 36 even and 21 odd couplings in our analysis. We find that the increase in the number of couplings has a significant influence on the largest eigenvalues of the linearized renormalization transformation matrices. These eigenvalues serve to estimate the renormalization exponents yI and yH. Remarkably, we find no significant finite-size effect on these eigenvalues when the maximum number of couplings is included in the analysis, except for the smallest system sizes (83 → 43). After a suitable extrapolation to the fixed point, we find good agreement with existing results for the critical exponents. We have determined the critical point of the simple cubic Ising model as K = 0.221652(6), also in agreement with existing results.

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