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Journals / Sakarya University Journal of Science / 2026 / Volume: 17 Issue: 1

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

Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi

Asaf Tolga Ülgen
Naci Sünel
Pages
—
Publication Date
2013-04-01
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AI Summary & Key Takeaways

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

The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics.
📊
Key Findings & Data:Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively.
💡
Conclusion & Impact:The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Blume-Capel Models · Phase Transitions · Bifurcation

Abstract

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.

Özet

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.

🔖

Cite This Article

Ülgen, A. T., Sünel, N. (2013). Solution of Macroscopic State Equations of Blume-Capel Model Using Nonlinear Dynamics Concepts. Sakarya University Journal of Science, Volume: 17 Issue: 1. https://doi.org/10.16984/saufbed.62612

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