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Critical Behaviour of the Ising S=l/2 and S=l Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices

Published online by Cambridge University Press:  20 August 2015

F. W. S. Lima*
Affiliation:
Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550 Teresina, Piauí, Brazil
J. Mostowicz*
Affiliation:
Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
K. Malarz*
Affiliation:
Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
*
Corresponding author.Email:[email protected]
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Abstract

We investigate the critical properties of the Ising S = 1/2 and S = 1 model on (3,4,6,4) and (34,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, and ν basing on finite size scaling analysis. The calculated values of the critical temperature for S = 1 are kBTC/J=1.590(3), and kBTC/J=2.100(4) for (3,4,6,4) and (34,6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν, and 1/ν, for S=1 are β/ν=0.180(20), γ/ν=1.46(8), and 1/ν=0.83(5), for (3,4,6,4) and 0.103(8), 1.44(8), and 0.94(5), for (34,6) Archimedean lattices. Obtained results differ from the Ising S = 1/2 model on (3,4,6,4), (34,6) and square lattice. The evaluated effective dimensionality of the system for S = 1 are Deff=1.82(4), for (3,4,6,4), and Deff = 1.64(5) for (34,6).

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Lenz, W., Z. Phys., 21 (1921), 613; Ising, E., Z. Phys., 31 (1925), 235.Google Scholar
[2]Baxter, R. J., Exactly solved models in statistical mechanics, London (1982), Academic Press.Google Scholar
[3]Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E., J. Chem. Phys., 21 (1953), 1087.Google Scholar
[4]Swendsen, R. H. and Wang, J. S., Phys. Rev. Lett., 58 (1987), 86.Google Scholar
[5]Wang, F. and Landau, D. P., Phys. Rev. Lett, 86 (2001), 2050.Google Scholar
[6]Ferrenberg, A. M. and Swendsen, R. H., Phys. Rev. Lett., 61 (1988), 2635.Google Scholar
[7]Oliveira, P. M. C. de, Penna, T. J. P. and Herrmann, H. J., Braz. J. Phys., 26 (1996), 677.Google Scholar
[8]Callen, E. and Shapero, D., Physics Today, 27 (1974), 23.Google Scholar
[9]Galam, S., Gefen, Y. and Shapir, Y., J. Mathematical Sociology, 9 (1982), 1.Google Scholar
[10]Latané, B., Am. Psychologist, 36 (1981), 343.Google Scholar
[11]Liggett, T. M., Interacting Particles Systems, Springer, New York (1985).Google Scholar
[12]Schelling, T. C., J. Mathematical Sociology, 1 (1971), 141.Google Scholar
[13]Stauffer, D., Oliveira, S. Moss. de, Oliveira, P. M. C. de and Martins, J. S. Sä, Biology, Sociology, Geology by Computational Physicists, Elsevier Amsterdam, (2006).Google Scholar
[14]Zaklan, G., Westerhoff, F. and Stauffer, D., J. Econ. Interact. Coord., 4 (2008), 1.Google Scholar
[15]Zaklan, G., Lima, F. W. S. and Westerhoff, F., Physica A, 387 (2008), 5857.Google Scholar
[16]Potts, R. B., Proc. Cambridge Phil. Soc., 48 (1952), 106.Google Scholar
[17]Wu, F.-Y., Rev. Mod. Phys., 54 (1982), 235.Google Scholar
[18]Blume, M., Phys. Rev., 141 (1966), 517.CrossRefGoogle Scholar
[19]Capel, H. W., Physica (Amsterdam), 32 (1966), 966.Google Scholar
[20]Saul, D. M., Wortis, M., Stauffer, D., Phys. Rev. B, 9 (1974), 4974.Google Scholar
[21]Jain, A. K., Landau, D. P., Phys. Rev. B, 22 (1980), 445.Google Scholar
[22]Bonfim, O. F. de Alcantara, Physica A, 130 (1985), 365.Google Scholar
[23]Berker, A. N., Wortis, M., Phys. Rev. B, 14 (1976), 4946.Google Scholar
[24]Oliveira, S. Moss de, Oliveira, P. M. C. de, Barreto, F. C. Sä, J. Stat. Phys., 78 (1995), 1619.Google Scholar
[25]Plascak, J. A., Moreira, J. G., Barreto, F. C. Sä, Phys. Lett. A, 173 (1993), 360.Google Scholar
[26]Tamashiro, M. N., Salinas, S. R., Physica A, 211 (1994), 124.Google Scholar
[27]Xavier, J. C., Alcaraz, F. C., Lara, D. Pen˜a, Plascak, J. A., Phys. Rev. B, 57 (1998), 11575.Google Scholar
[28]Lara, D. Peña, Plascak, J. A., Int. J. Mod. Phys. B, 12 (1998), 2045.Google Scholar
[29]Barreto, F. C. Sä, Bonfim, O. F. Alcantara, Physica A, 172 (1991), 378.Google Scholar
[30]Bakchinch, A., Bassir, A., Benyoussef, A., Physica A, 195 (1993), 188.Google Scholar
[31]Plascak, J. A., Landau, D. P., Phys. Rev. E, 67 (2003), R015103.Google Scholar
[32]Lima, F. W. S., Int. J. Mod. Phys. C, 17 (2006), 1267.Google Scholar
[33]Kepler, J., Harmonices Mundi (Lincii) (1619).Google Scholar
[34]Suding, P. N., Ziff, R. M., Phys. Rev. E, 60 (1999), 275Google Scholar
[35]Malarz, K., Zborek, M., Wröbel, B., TASK Quartely, 9 (2005), 475.Google Scholar
[36]Lima, F. W. S., Malarz, K., Int. J. Mod. Phys. C, 17 (2006), 1273.Google Scholar
[37]Landau, D. P., Binder, K., A Guide to Monte Carlo Simulations in Statistical Physics, 2nd edition, Cambridge UP, 2005.Google Scholar
[38]Binder, K., Z. Phys. B, 43 (1981), 119.Google Scholar
[39]Blöte, H. W. J. and Nightingale, M. P., Physica A, 134 (1985), 274.Google Scholar
[40]Mostowicz, J., M.Sc. Thesis, AGH-UST, Kraków (2009).Google Scholar
[41]Codello, A., J. Phys. A: Math. Theor., 43 (2010), 385002; ibid 399801.Google Scholar