Abstract
Using a transfer matrix technique and the Ising model, the predictions of the MFRG concept for clusters with linear size up to 21 have been tested for the three-cluster MFRG approach. Even for small sizes of the clusters, the three-cluster estimates of critical couplings and bulk critical exponents give the accuracy level equal to that of two-cluster renormalization for much greater sizes. Performing the asymptotic analysis for the new data, the convergence of the surface critical exponent yhs towards the exact value is illustrated for the first time. Our improved method has enabled us to obtain the results for clusters with substantially greater sizes, to accelerate the calculations and also to confirm the reliability of the MFRG approach for the Ising model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)