Araştırma Makalesi
BibTex RIS Kaynak Göster

Solution of Macroscopic State Equations of Blume-Capel Model Using Nonlinear Dynamics Concepts

Yıl 2013, Cilt: 17 Sayı: 1, 53 - 60, 01.04.2013

Öz

The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.

Kaynakça

  • Cooke A H, Martin D and Wells M R, Solid State Commun 9, 519 (1971).
  • Sayetat F, Boucherle J X, Belakhovsky M, Kallel A, Tcheou F and Fuess H, Phys. Letters 35A , 361 (1971).
  • Capel H W, Physica 32, 966 (1966).
  • Blume M, Phys. Rev. 141, 517 (1966).
  • Siqueira A E, Fittipaldi I P, Physica A 138, 599 (1986).
  • Tanaka Y, Uryˆu N, J. Phys. Soc. Japan 50, 1140 (1981).
  • Saul D M, Wortis M, Stauffer D, Phys. Rev. B 9, 4964 (1974).
  • Berker A N, Wortis M, Phys. Rev. B 14, 4946 (1976).
  • Arora B L, Landau D P, Proc. AIP 5, 352 (1972).
  • Takanaka M, Takahashi K, Phys. Stat. Sol. B 93, K85 (1979).
  • Ng W M, Barry J H, Phys Rev B 17, 3675 (1978).
  • Ekiz C, Keskin M, Yalçın O, Physica A 293, 215 (2001).
  • Keskin M, Ekiz C, Yalçın O, Physica A 267, 392 (1999).
  • Keskin M, Özgan Ş, Physica Scriptia 42, 349 (1990).
  • Özsoy O, Keskin M, Physica A 319, 404 (2003).
  • Cotton F A, The Crystal Field Theory. Chemical Applications of Group Theory, 3nd ed. (John Wiley& Sons, New York, 1990).
  • Kuang X Y, Phys. Lett. A 213, 89 (1996).
  • Thompson J M T, Stewart H B, Nonlinear Dynamics and Chaos, 2nd ed. (John Wiley& Sons, 2002).
  • Schuster H G, Just W, Deterministic Chaos, (Wiley-VCH Verlag, Weinheim, 2005).
  • Wigger G A, Felder E, Monnier R, and Ott H R, Pham L, Fisk Z, Phys. Rev. B, 014419 (2005).
  • Rößler S, Harikrishnan, Naveen Kumar C M, Bhat H L, Elizabeth Suja, Rößler U K, Steglich F, Wirth S, J Supercond Nov Magn 22, 205208 (2009).

Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi

Yıl 2013, Cilt: 17 Sayı: 1, 53 - 60, 01.04.2013

Öz

The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.

Kaynakça

  • Cooke A H, Martin D and Wells M R, Solid State Commun 9, 519 (1971).
  • Sayetat F, Boucherle J X, Belakhovsky M, Kallel A, Tcheou F and Fuess H, Phys. Letters 35A , 361 (1971).
  • Capel H W, Physica 32, 966 (1966).
  • Blume M, Phys. Rev. 141, 517 (1966).
  • Siqueira A E, Fittipaldi I P, Physica A 138, 599 (1986).
  • Tanaka Y, Uryˆu N, J. Phys. Soc. Japan 50, 1140 (1981).
  • Saul D M, Wortis M, Stauffer D, Phys. Rev. B 9, 4964 (1974).
  • Berker A N, Wortis M, Phys. Rev. B 14, 4946 (1976).
  • Arora B L, Landau D P, Proc. AIP 5, 352 (1972).
  • Takanaka M, Takahashi K, Phys. Stat. Sol. B 93, K85 (1979).
  • Ng W M, Barry J H, Phys Rev B 17, 3675 (1978).
  • Ekiz C, Keskin M, Yalçın O, Physica A 293, 215 (2001).
  • Keskin M, Ekiz C, Yalçın O, Physica A 267, 392 (1999).
  • Keskin M, Özgan Ş, Physica Scriptia 42, 349 (1990).
  • Özsoy O, Keskin M, Physica A 319, 404 (2003).
  • Cotton F A, The Crystal Field Theory. Chemical Applications of Group Theory, 3nd ed. (John Wiley& Sons, New York, 1990).
  • Kuang X Y, Phys. Lett. A 213, 89 (1996).
  • Thompson J M T, Stewart H B, Nonlinear Dynamics and Chaos, 2nd ed. (John Wiley& Sons, 2002).
  • Schuster H G, Just W, Deterministic Chaos, (Wiley-VCH Verlag, Weinheim, 2005).
  • Wigger G A, Felder E, Monnier R, and Ott H R, Pham L, Fisk Z, Phys. Rev. B, 014419 (2005).
  • Rößler S, Harikrishnan, Naveen Kumar C M, Bhat H L, Elizabeth Suja, Rößler U K, Steglich F, Wirth S, J Supercond Nov Magn 22, 205208 (2009).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Asaf Tolga Ülgen Bu kişi benim

Naci Sünel Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2013
Gönderilme Tarihi 19 Eylül 2012
Kabul Tarihi 6 Kasım 2012
Yayımlandığı Sayı Yıl 2013 Cilt: 17 Sayı: 1

Kaynak Göster

APA Ülgen, A. T., & Sünel, N. (2013). Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi. Sakarya University Journal of Science, 17(1), 53-60. https://doi.org/10.16984/saufbed.62612
AMA Ülgen AT, Sünel N. Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi. SAUJS. Nisan 2013;17(1):53-60. doi:10.16984/saufbed.62612
Chicago Ülgen, Asaf Tolga, ve Naci Sünel. “Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi”. Sakarya University Journal of Science 17, sy. 1 (Nisan 2013): 53-60. https://doi.org/10.16984/saufbed.62612.
EndNote Ülgen AT, Sünel N (01 Nisan 2013) Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi. Sakarya University Journal of Science 17 1 53–60.
IEEE A. T. Ülgen ve N. Sünel, “Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi”, SAUJS, c. 17, sy. 1, ss. 53–60, 2013, doi: 10.16984/saufbed.62612.
ISNAD Ülgen, Asaf Tolga - Sünel, Naci. “Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi”. Sakarya University Journal of Science 17/1 (Nisan 2013), 53-60. https://doi.org/10.16984/saufbed.62612.
JAMA Ülgen AT, Sünel N. Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi. SAUJS. 2013;17:53–60.
MLA Ülgen, Asaf Tolga ve Naci Sünel. “Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi”. Sakarya University Journal of Science, c. 17, sy. 1, 2013, ss. 53-60, doi:10.16984/saufbed.62612.
Vancouver Ülgen AT, Sünel N. Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi. SAUJS. 2013;17(1):53-60.

30930 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.