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physica status solidi (b)

Two‐step mean‐field renormalization group results for the large square Ising clusters

G. Kamieniarz, Grzegorz Musiał, Daria M. Tomecka

Published Mar 1, 2003• 1 citation
Publisher

Abstract

Abstract A transfer matrix approach has been worked out to test the predictions of the improved three‐step mean‐field renormalization group approach to square Ising clusters with linear size up to L = 11. Performing the asymptotic analysis, the convergence of the finite‐size critical couplings and the critical exponents towards the exact values is shown.

DOI
10.1002/pssb.200301711

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Abstract A transfer matrix approach has been worked out to test the predictions of the improved three‐step mean‐field renormalization group approach to square Ising clusters with linear size up to L = 11. Performing the asymptotic analysis, the convergence of the finite‐size critical couplings and the critical exponents towards the exact values is shown.
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The recently proposed multi-interaction mean-field renormalization technique [C. N. Likos and A. Maritan, Phys. Rev. E 53, 3303 (1996)] is applied to the Ising model on a triangular lattice with equal couplings in two directions and a different coupling in the third, a model equivalent to a square Ising model with additional second-neighbor interactions along a single diagonal direction. Three different clusters are considered and the possible mappings between them are discussed. The estimates for critical couplings and exponents are in satisfactory agreement with exact results. An explanation of the way in which the finite-size features of the method bring about a systematic overestimation of the critical temperature is also given.