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ISING MODELDE KORELASYONLU İNDİRGENMİŞ TRANSFER MATRİS YAKLAŞIMI

CORRELATED REDUCED TRANSFER MATRIX APPROACH FOR ISING MODEL

Journal Name:

  • İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi

Publication Year:

  • 2008

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this work we try to improve 2D reduced transfer matrix aproach and critical coupling strenght, Kc=J/kBT, using many-body correlated function. For this aim we replace local spin degrees of freedom with many body correlated function, σi,j+1= <σ> + λ(σi,j - <σ>), instead of magnetization per spin, (<σ>), in the Hamiltonyen. In this function we take λ= 1/(z-1)=1/3, where z is the coordination number. Kc=J/kBT of 2D Ising model in reduced transfer matrix aproach is 0.401. However correlated reduced transfer matrix approach supposes Kc=J/kBT=0.455. This result deviates from the exact value obtained by Onsager by 3.4 percent
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Abstract (Original Language): 
Bu çalışmada 2 boyutlu indirgenmiştransfer matris yaklaşımı, çok parçacıklı korelasyon fonksiyonu kullanılarak geliştirilmeye ve daha iyi bir Kc=J/kBT değeri elde edilmeye çalışılmıştır. Bunun için Hamiltonyendeki spinler, ortalama spin manyetizasyonu, (<σ>), yerine çok parçacıklı korelasyon fonksiyonu, σi,j+1= <σ> + λ(σi,j - <σ>), ile yer değiştirilmiştir. Burada z, koordinasyon sayısı olmak üzere λ=1/(z-1)=1/3 alınmıştır. İndirgenmiştransfer matris yaklaşımının 2 boyutlu Ising ferromanyetiği için tahmin ettiği Kc=J/kBT değeri 0.401’dir. Korelasyonlu indirgenmiştransfer matris metodunun tahmin ettiği değer ise Kc=J/kBT=0.455’ dir. Bu değer L. Onsager’in bulduğu gerçek değerden sadece % 3.4 farklıdır.
FULL TEXT (PDF): 
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  • 14
73-84
  • Turkish

REFERENCES

References: 

Baxter R. J., (1989), Exactly Solved Models in Statistical Mechanics, 3th. Ed.,
London, Academic Press Limited
Bethe H. A., (1935), “Statistical Theory of Superlattices”, Proc. Roy. Soc. London
Ser., A 150,552-575
Bragg W.L., Williams E.J., (1935), “The Effect of Thermal Agitation on Atomic
Arrangement in Alloys”,Proc. Roy. Soc. London Ser., A 145,699-730
İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi Güz 2008/2
83
Callen H.B., (1963), “A Note on Green Functions andthe Ising Model”, Phys. Lett.
4, 161-161
Domb C., (1960), Adv. Phys.9, “On the Theory of Cooperatif Phenomena”, 149-361
Fisher M.E., (1974), “The Renormalization Group in the Theory of Critical
Behavior”, Rev. Mod. Phys. 46, 597-616
Honmura R., (1984), “Correlated-Effective-Field Treatment of the Anisotropic Ising
Ferromagnet: Thermodynamical Properties”, Phys. Rev. B 30,348-358
Honmura R., Kaneyoshi T. (1979), “ Contribution to the New Type of Effective-Field Theory of the Ising Model”, J. Phys. C 12, 3979-3992
Ising E., (1925), “Beitrag zur Theorie des Ferromagnetismus”, Zeits f. Physik, 31,
253-258
Kadanoff L.P. vd., (1967), “Static Phenomena Near Critical Points: Theory and
Experiment”, Rev. Mod. Phys. 39, 395-431
Kaneyoshi T., Fittipaldi I.P, Honmura R., Manabe T., (1981), “New Correlated-Effective-Field Theory in the Ising Model”, Phys. Rev. B 24, 481-484
Kaya T. ve Arık M.M., (2009), “Reduced Transfer Matrix Approach in Ising
Model”, International Journal of Modern Physics B, (Kabul Edildi).
Kramers H. A., Wannier G. H., (1941), “Statistics of the Two-Dimensional
Ferromagnet. Part I”, Phys. Rev. 60, 252-262
Lines M.E., (1974), “Many-Body Theory of Magnetism for Ions With Complicated
Level Structure ”, Phys. Rev. B 9, 3927-3931
Maris H.J., Kadanoff L. P., (1978), Am. J. Phys. 46(6), 652-657
Onsager L., (1944), “Crystal Statistics. I. A Two Dimensional Model with an Order-Disorder Transition”, Phys. Rev. 65, 117-149
Peierls R., (1936), “Ising Model of Magnetism”, Proc. Cambridge Philos. Soc. B2,
477-481
Smart J. S., 1966, Effective Field Theories of Magnetism, Philadelpia, W.B.
Saunders Co.,
Tuncer KAYA, Murat ARIK
84
Streb B., Callen H. B., Horwitz G., (1963), “Cluster Expansion for the Heisenberg
Ferromagnet”, Phys. Rev. 130, 1798-1808
Sykes M. F., Gaunt D. S., Roberts P.D., Wyley J.A.,(1972), “High Temperatures for
the Susceptibility of the Ising Model II. Three Dimensional Lattices”, J. Phys. A bf
5, 640-652
Taggart G.B., (1982), “Correlated Effective Field Approximation for the Dilute
Ising Ferromagnet”, Physica 116A, 34-44
Weiss P., (1907), “The Hypothesis of the Molecular Field and the Property of
Ferromagnetism”, J. Phys. 6, 661-674
Wilson K.G., (1983), “The Renormalization Group andCritical Phenomena”, Rev.
Mod. Phys. 55, 583-600
Wilson K.G., (1971), “Renormalization Group and Critical Phenomena. I.
Renormalization Group and the Kadanoff Scaling Picture”, Phys. Rev. B 4, 3174-3183
Wysin G.M. ve Kaplan J., (2000), “Correlated Molecular-Field Theory for Ising
Models”, Phys. Rev. E 61, 6399-6403

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