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Transfer‐matrix study of critical properties of the Ising model following from the three‐cluster MFRG approach
Author(s) -
Kamieniarz Grzegorz,
Tomecka Daria M.
Publication year - 2006
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200562469
Subject(s) - ising model , cluster (spacecraft) , critical exponent , statistical physics , exponent , convergence (economics) , transfer matrix , matrix (chemical analysis) , renormalization , renormalization group , transfer matrix method (optics) , physics , mathematics , condensed matter physics , computer science , mathematical physics , materials science , quantum mechanics , phase transition , linguistics , philosophy , economic growth , economics , composite material , computer vision , programming language
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 y hs 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)