The Finite-Size Scaling Study of the Ising Model for the Fractals

详细信息    查看全文

• 作者：Z. Merdan ; M. Bayirli ; A. Günen ; M. Bülbül
• 关键词：Ising model ; Finite ; size scaling ; Cellular automaton ; Fractals
• 刊名：International Journal of Theoretical Physics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：55
• 期：4
• 页码：2031-2039
• 全文大小：1,023 KB
• 参考文献：1.Witten, T.A., Sander, L.M.: Phys. Rev. Lett. 47, 1400 (1980)ADS CrossRef
  2.Witten, T.A., Sander, L.M.: Phys. Rev. B. 27, 5686 (1983)ADS MathSciNet CrossRef
  3.Vicsek, T.: Fractal Growth Phenomena Word Scientific Singapore (1989)
  4.Mandelbrot, B.B., Frame, M.: Fractals Encyclopedia of Physical Science and Technology (San Francisco: Academic) (1982)
  5.Mandelbrot, B.B. An Introduction to Multifractal Distribution Functions in Random Fluctuations and Pattern Growth: Experiment and Models. In: Stanley, HE, Ostrowsky, N (eds.) . Kluwer, Dordrecht (1988)
  6.Merdan, Z., Bayirli, M.: Chin. Phys. Lett. 22, 2112 (2005)ADS CrossRef
  7.Forrest, S.R., Witten, T.A.: J. Phys. A Math. Gen. 12, L109 (1979)ADS CrossRef
  8.Family, F., Masters, B.R.: D Platt Physica D 38, 98 (1989)ADS CrossRef
  9.Niemeyer, L., Pietrenero, L., Wiesmann , H.J.: Phys. Rev. Lett. 12(1033), 52 (1984)
  10.Matsushita, M., Sano, M., Hanjo, H., Savada, Y.: Phys. Rev. Lett. 3 (286), 53 (1984)
  11.Fijikawa, H., Matsushita, M.: J. Phys. Soc. Japan 11(3875), 58 (1989)
  12.Huang, S.Y., Zou, X.W., Tan, Z.J., Jin, Z.Z.: Phys. Lett. A 292, 141 (2001)ADS CrossRef
  13.Tan, Z.J., Zou, X.-W., Jin, Z.Z.: Phys. Lett. A 282, 121 (2001)ADS CrossRef
  14.Lattuada, M., Wu, H., Mordibelli, M.: J. Coll. Int. Scienc. 268, R106 (2003)CrossRef
  15.Creutz, M.: Ann. Phys. 167, 62 (1986)ADS CrossRef
  16.Privman, V. (ed.): Finite Size Scaling and Numerical Simulation of Statistical Systems Word Scientific Singapore (1990)
  17.Kutlu, B., Aktekin, N.: J. Stat. Phys. 75, 757 (1994)ADS CrossRef
  18.Kutlu, B., Aktekin, N.: Physica A 208, 423 (1994)ADS CrossRef
  19.Kutlu, B., Aktekin, N.: Physica A 215, 370 (1995)ADS CrossRef
  20.Kutlu, B.: Phyica A 243, 199 (1997)ADS CrossRef
  21.Aktekin, N.: Physica A 219, 436 (1995)ADS CrossRef
  22.Aktekin, N.: Physica A 232, 397 (1996)ADS CrossRef
  23.Aktekin, N. in: Annual Reviews of Computational Physics vol. VII. In: Stauffer, D (ed.) , p 1. Word Scientific, Singapore (2000)
  24.Aktekin, N.: Physica 215, 397 (1996)CrossRef
  25.Vichniac, G.Y.: Physica D 10, 96 (1984)ADS MathSciNet CrossRef
  26.Pomeau, Y.: J. Phys. A 17, L145 (1984)MathSciNet CrossRef
  27.Hermann, H.J.: J. Stat. Phys. 45, 145 (1986)ADS CrossRef
  28.Lang, W.M., Stauffer, D.: J. Phys. A 20, 5413 (1987)ADS MathSciNet CrossRef
  29.Merdan, Z., Boyacıoğlu, B., Günen, A., Sağlam, Z.: Bull. Pur. And Appl. Scienc. 22, D95 (2003)
  30.Merdan, Z., Günen, A., Mülazımoğlu, G.: Int. J. Mod. Phys. C 16, 1269 (2005)ADS CrossRef
  31.Merdan, Z., Günen, A., Çavdar, Ş.: Physica A 359, 415 (2006)ADS CrossRef
  32.Merdan, Z., Erdem, R.: Phys. Lett. A 330, 403 (2004)ADS CrossRef
  33.Merdan, Z., Bayırlı, M.: Appl. Math. Comp. 167, 212 (2005)CrossRef
  34.Merdan, Z., Duran, A., Atille, D., Mülazımoğlu, G., Günen, A.: Physica A 366, 265 (2006)ADS CrossRef
  35.Merdan, Z., Atille, D.: Physica A 376, 327 (2007)ADS CrossRef
  36.Merdan, Z., Atille, D.: Mod. Phys Lett. B 21, 215 (2007)ADS CrossRef
  37.Mülazimoglu, G., Duran, A., Merdan, Z., Günen, A.: Mod. Phys. Lett. B 13, 1329 (2008)CrossRef
  38.Merdan, Z, Bayirli, M., Oztürk, M.K.: Zeitschrift für Naturforschung A 64a, 849 (2009)ADS
  39.Merdan, Z., Bayirli, M., Oztürk, M.K.: Zeitschrift für Naturforschung A 65a, 705 (2010)ADS
  40.Merdan, Z., Guzelsoy, E.: Low Tempetarure Physics 37, 470 (2011)ADS CrossRef
  41.Merdan, Z., Guzelsoy, E.: Int. J. Theor. Phys. 51, 1621 (2012)CrossRef
  42.Baxter, R.B.: Exactly Solved Modern Statistical Mechanics. Oxford University Press, Oxford (1989)
  43.Hahne, F.J.W.: Critical Phenomena, Proceedings, Stellenbosch. Springer-Verlag, Berlin (1983)CrossRef MATH
  44.Huang: Exactly Solved Modern Statistical Mechanics. Oxford University Press (1989)
  45.Zhang, Z.D., March, N.H.: J. Math. Chem. 50, 920 (2012)MathSciNet CrossRef
  
• 作者单位：Z. Merdan (1)
  M. Bayirli (2)
  A. Günen (1)
  M. Bülbül (1)
  
  1. Faculty of Arts and Sciences, Department of Physics, Gazi University, Ankara, Turkey
  2. Faculty of Arts and Sciences, Department of Physics, Balikesir University, Balikesir, Turkey
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Elementary Particles and Quantum Field Theory
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9575

文摘

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and \(d_{f}^{\beta } =1.876(8), \,d_{f}^{\gamma } =3.747(10), \,d_{f}^{\alpha } =2.081(68), \,d_{f}^{\delta } =1.940(22)\), \(d_{f}^{\eta } =2.178(10)\), \(d_{f}^{\nu } =2.960(22)\), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and \(d_{f}^{\beta } =1.875, \,d_{f}^{\gamma } =3.75, \,d_{f}^{\alpha } =2, \,d_{f}^{\delta } =1.933, \,d_{f}^{\eta } =2.25, \,d_{f}^{\nu } =3\).