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Journals / Selçuk Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi / 2004 / Sayı: 23

Investigation of the well know finite-size scaling function and finite-size scaling functions with logarithmic correction for the four dimensional Ising model

Dört boyutlu Ising model için bilinen sonlu örgü ölçekleme ve logaritmik düzeltmeli sonlu örgü ölçekleme fonksiyonlarının incelenmesi

Ziya MERDAN
Mehmet BAYIRLI
Abdullah GÜNEN
Pages
33–43
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Similarity, the exponents for the specific heat (C) are calculated as $frac{alpha}{nu}$ = 0.0932, $frac{alpha}{nu}$ =-0.1055 with the logarithmic factor and $frac{alpha}{nu}$ = —0.0715 without logaritmic factor.These results are in good agreement with the results of simulations with three-bit demons and theoretical values.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:Critical exponents of the magnetic susceptibility $(chi)$ is found as $frac{gamma}{nu}$= 2.0057 when the expression with the logarithmic factor is used and as $frac{gamma}{nu}$ — 2.2529 when the expression without logarithmic factor is used.
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Conclusion & Impact:Similarity, the exponents for the specific heat (C) are calculated as $frac{alpha}{nu}$ = 0.0932, $frac{alpha}{nu}$ =-0.1055 with the logarithmic factor and $frac{alpha}{nu}$ = —0.0715 without logaritmic factor.These results are in good agreement with the results of simulations with three-bit demons and theoretical values.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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 $(chi)$ is found as $frac{gamma}{nu}$= 2.0057 when the expression with the logarithmic factor is used and as $frac{gamma}{nu}$ — 2.2529 when the expression without logarithmic factor is used. Similarity, the exponents for the specific heat (C) are calculated as $frac{alpha}{nu}$ = 0.0932, $frac{alpha}{nu}$ =-0.1055 with the logarithmic factor and $frac{alpha}{nu}$ = —0.0715 without logaritmic factor.These results are in good agreement with the results of simulations with three-bit demons and theoretical values.

Özet

Dört boyutlu Ising modelinin, doğrusal boyutu L =4,6,8,10,12,14,16 olan periyodik sınır şartlı soyut basit küp örgülerde, dört "bit"li demonlar kullanılarak Creutz cellular automaton'ında simülasyonu yapıldı. Simülasyondan elde edilen veriler bilinen sonlu örgü olçekleme teorisi ve logaritmik düzeltmeli sonlu örgü olçekleme teorisine göre analiz edildi. Manyetik alınganlık için kritik üs logaritmik düzeltme olmaksızın $frac{gamma}{nu}$= 2.2529 logaritmik düzeltmeli $frac{gamma}{nu}$ = 2.0057, özısı için kritik üs logaritmik düzeltme olmaksızın $frac{alpha}{nu}$-0.0715 logaritmik düzeltmeli $frac{alpha}{nu}$= 0.0932 $frac{alpha}{nu}$= -0.1055 elde edildi. Bu sonuçlar üç "bit"li demonlar kullanılarak yapılan simülasyon sonuçları ve teorik değerlerle uyum halindedir.

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Cite This Article

MERDAN, Z., BAYIRLI, 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. Selçuk Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, Sayı: 23, 33–43. https://ajindex.com/articles/317593

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