VERIFICATION OF THE THREE-CLUSTER MOLECULAR-FIELD RENORMALIZATION GROUP APPROACH FOR THE ISING MODEL
Kamieniarz Grzegorz, Musiał Grzegorz
Computational Physics Division, Institute of Physics,
A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
Received:
Received 25 January 2002
DOI: 10.12921/cmst.2002.08.01.63-67
OAI: oai:lib.psnc.pl:528
Abstract:
A transfer matrix approach has been worked out to test the predictions of the three-step molecular-field renormalization group (MFRG) for square Ising clusters with linear size up to L = 11. The convergence of the finite-size critical couplings and the critical exponents towards the exact values is shown.
References:
[1] J. O. Indekeu, A. Maritan, A. Stella, J. Phys. A15, L291 (1982).
[2] J. O. Indekeu, A. Maritan, A. Stella, Phys. Rev. B35, 305 (1987).
[3] I. P. Fittipaldi, J. Magn. Magn. Mat. 131, 43 (1994).
[4] K. Croes, J. O. Indekeu, Mod. Phys. Lett. B7, 699 (1993).
[5] J. A. Plascak, W. Figueiredo, B. C. S. Grandi, Braz. J. Phys. 29, 579 (1999).
[6] C. N. Likos, Phys. Rev. E55, 2001 (1997).
[7] P. Pawlicki, G. Musiał, G. Kamieniarz, J. Rogiers, Physica A242, 281 (1997).
[8] J. R. de Sousa, I. G. Araujo, J. A. Plascak, Physica A278, 181 (2000).
[9] D. P. Lara, J. A. Plascak, Int. J. Mod. Phys. B12, 1831 (1998).
[10] P. A. Slotte, J. Phys. A20, L177 (1987).
[11] G. Kamieniarz, R. Dekeyser, Symmetry and Structural Properties of Condensed Matter,
ed. W. Florek, D. Lipiński and T. Lulek, World Scientific, Singapore 1993, p. 181.
[12] G. Kamieniarz, H. W. J. Blöte, J. Phys. A26, 201 (1993).
[13] M. N. Barber, Phase Transitions and Critical Phenomena, vol. 8, ed. C. Domb and J. L. Lebowitz, Academic Press London, 1983, p. 145.
A transfer matrix approach has been worked out to test the predictions of the three-step molecular-field renormalization group (MFRG) for square Ising clusters with linear size up to L = 11. The convergence of the finite-size critical couplings and the critical exponents towards the exact values is shown.
[1] J. O. Indekeu, A. Maritan, A. Stella, J. Phys. A15, L291 (1982).
[2] J. O. Indekeu, A. Maritan, A. Stella, Phys. Rev. B35, 305 (1987).
[3] I. P. Fittipaldi, J. Magn. Magn. Mat. 131, 43 (1994).
[4] K. Croes, J. O. Indekeu, Mod. Phys. Lett. B7, 699 (1993).
[5] J. A. Plascak, W. Figueiredo, B. C. S. Grandi, Braz. J. Phys. 29, 579 (1999).
[6] C. N. Likos, Phys. Rev. E55, 2001 (1997).
[7] P. Pawlicki, G. Musiał, G. Kamieniarz, J. Rogiers, Physica A242, 281 (1997).
[8] J. R. de Sousa, I. G. Araujo, J. A. Plascak, Physica A278, 181 (2000).
[9] D. P. Lara, J. A. Plascak, Int. J. Mod. Phys. B12, 1831 (1998).
[10] P. A. Slotte, J. Phys. A20, L177 (1987).
[11] G. Kamieniarz, R. Dekeyser, Symmetry and Structural Properties of Condensed Matter,
ed. W. Florek, D. Lipiński and T. Lulek, World Scientific, Singapore 1993, p. 181.
[12] G. Kamieniarz, H. W. J. Blöte, J. Phys. A26, 201 (1993).
[13] M. N. Barber, Phase Transitions and Critical Phenomena, vol. 8, ed. C. Domb and J. L. Lebowitz, Academic Press London, 1983, p. 145.
