[figure: 9.7 cm]

VERIFICATION OF THE THREE-CLUSTER MEAN-FIELD RENORMALIZATION GROUP APPROACH FOR THE ISING MODEL

G. Kamieniarz, G. Musiał, D. Tomecka

Institute of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań,

                       Poland, e-mail: gjk@amu.edu.pl

The mean-field renormalization group (MFRG) method of computation of non-classical critical properties of lattice models is attractive [1] because of its efficiency and simplicity, and because it is easily applicable to bulk critical phenomena as well as to surface, random and dynamic effects. The consequences of its basic assumptions are analysed previously [2] using the two-cluster approach and sequences of cluster sizes L ≤ 11 which were not large enough to get the definite conclusions. Here, a modified transfer matrix approach has been worked out to test the predictions of the improved three-step MFRG method [1] for square Ising clusters as large as L = 18. Performing the asymptotic analysis, the convergence of the finite-size critical couplings and the critical exponents towards the exact values is shown.

[1] K. Croes, J.O. Indekeu, Mod. Phys. Lett. B7, 699 (1993)

[2] G. Kamieniarz, Physica A256, 211 (1999)

[figure: 13.4 cm]

Subject category :

5. Phase Transitions and Critical Phenomena

Presentation mode : oral

Corresponding author : G. Kamieniarz

Address for correspondence : Institute of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland

Email address : gjk@amu.edu.pl