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Dört Boyutlu Ising Model için Bilinen Sonlu Örgü Ölçekleme ve Logaritmik Düzeltmeli Sonlu Örgü Ölçekleme Fonksiyonlarının İncelenmesi

Year 2004, Volume: 1 Issue: 23, 33 - 44, 01.12.2004

Ziya Merdan Mehmet Bayırlı Abdullah Günen

Abstract

Dört boyutlu Ising modelinin, dorusal boyutu L =4,6,8,10,12,14,16 olan periyodik sınır artlı soyut basit küp örgülerde, dört “bit”li demonlar kullanılarak Creutz cellular automaton’ında simülasyonu yapıldı. Simülasyondan elde edilen veriler bilinen sonlu örgü ölçekleme teorisi ve logaritmik düzeltmeli sonlu örgü ölçekleme teorisine göre analiz edildi. Manyetik alınganlık için kritik üs logaritmik düzeltme olmaksızın ν γ = 2.2529 logaritmik düzeltmeli ν γ = 2.0057, özısı için kritik üs logaritmik düzeltme olmaksızın α ν = -0.0715 logaritmik düzeltmeli α ν = 0.0932 α ν = -0.1055 elde edildi. Bu sonuçlar üç “bit”li demonlar kullanılarak yapılan simülasyon sonuçları ve teorik deerlerle uyum halindedir.

Keywords

Ising Model Sonlu Örgü Ölçekleme Teorisi Cellular Automaton

Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model

Year 2004, Volume: 1 Issue: 23, 33 - 44, 01.12.2004

Ziya Merdan Mehmet Bayırlı Abdullah Günen

Abstract

The four-dimensional nearest-neighbor Ising model is simulated on the Creutz cellular automaton by using four-bit demons and the finite-size lattices with the linear dimension L=4,6,8,10,12,14,16. The simulation results for the finite-lattice are analyzed according to the conventional finite-size scaling theory with and without logarithmic factors. Critical exponents of the magnetic susceptibility ( χ ) is found as = .2 0057 ν γ when the expression with the logarithmic factor is used and as = .2 2529 ν γ when the expression without logarithmic factor is used. Similarity, the exponents for the specific heat (C ) are calculated as = .0 0932 ν α , = − .0 1055 ν α with the logarithmic factor and = − .0 0715 ν α without logaritmic factor.These results are in good agreement with the results of simulations with three-bit demons and theoretical values.

Keywords

Ising model Finite-Size Scaling Theory Cellular Automata

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Details

Other ID JA58PJ36VE
Authors

Ziya Merdan This is me

Mehmet Bayırlı This is me

Abdullah Günen This is me

Submission Date December 1, 2004
Publication Date December 1, 2004
Published in Issue Year 2004 Volume: 1 Issue: 23

Cite

APA Merdan, Z., Bayırlı, M., & Günen, A. (2004). Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model. Selcuk University Journal of Science Faculty, 1(23), 33-44.
AMA Merdan Z, Bayırlı M, Günen A. Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model. Selcuk University Journal of Science Faculty. December 2004;1(23):33-44.
Chicago Merdan, Ziya, Mehmet Bayırlı, and Abdullah Günen. “Investigation of the Well Know Finite-Size Scaling Function and Finite-Size Scaling Functions With Logarithmic Correction for the Four Dimensional Ising Model”. Selcuk University Journal of Science Faculty 1, no. 23 (December 2004): 33-44.
EndNote Merdan Z, Bayırlı M, Günen A (December 1, 2004) Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model. Selcuk University Journal of Science Faculty 1 23 33–44.
IEEE Z. Merdan, M. Bayırlı, and A. Günen, “Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model”, Selcuk University Journal of Science Faculty, vol. 1, no. 23, pp. 33–44, 2004.
ISNAD Merdan, Ziya et al. “Investigation of the Well Know Finite-Size Scaling Function and Finite-Size Scaling Functions With Logarithmic Correction for the Four Dimensional Ising Model”. Selcuk University Journal of Science Faculty 1/23 (December2004), 33-44.
JAMA Merdan Z, Bayırlı M, Günen A. Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model. Selcuk University Journal of Science Faculty. 2004;1:33–44.
MLA Merdan, Ziya et al. “Investigation of the Well Know Finite-Size Scaling Function and Finite-Size Scaling Functions With Logarithmic Correction for the Four Dimensional Ising Model”. Selcuk University Journal of Science Faculty, vol. 1, no. 23, 2004, pp. 33-44.
Vancouver Merdan Z, Bayırlı M, Günen A. Investigation of the well Know Finite-Size Scaling Function and Finite-Size Scaling Functions with Logarithmic Correction for the Four Dimensional Ising Model. Selcuk University Journal of Science Faculty. 2004;1(23):33-44.

Journal Owner: On behalf of Selçuk University Faculty of Science, Rector Prof. Dr. Hüseyin YILMAZ
Selcuk University Journal of Science Faculty accepts articles in Turkish and English with original results in basic sciences and other applied sciences. The journal may also include compilations containing current innovations.

It was first published in 1981 as "S.Ü. Fen-Edebiyat Fakültesi Dergisi" and was published under this name until 1984 (Number 1-4).
In 1984, its name was changed to "S.Ü. Fen-Edeb. Fak. Fen Dergisi" and it was published under this name as of the 5th issue.
When the Faculty of Letters and Sciences was separated into the Faculty of Science and the Faculty of Letters with the decision of the Council of Ministers numbered 2008/4344 published in the Official Gazette dated 3 December 2008 and numbered 27073, it has been published as "Selcuk University Journal of Science Faculty" between 2009-2025. 
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