Beg Spin Camının Global Faz Diyagramları Ve Spinsiz Fermiyon Sistemleri
Beg Spin Camının Global Faz Diyagramları Ve Spinsiz Fermiyon Sistemleri
Dosyalar
Tarih
07.07.2008
Yazarlar
Özçelik, Veli Ongun
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Bu tez sürecinde klasik ve kuantum sistemlerde meydana gelen faz geçişleri üzerinde durularak Blume-Emery-Griffiths ve Hubbard modelleri üzerinde uygulamalar yapılmıştır. Blume-Emery-Griffiths spin camı modelinin global faz diyagramları hesaplanarak bu gaz diyagramı üzerindeki faz sınırları incelenmiş; birince ve ikinci dereceden faz geçişlerini ayıran trikritik noktanın sıcaklığa olan ters bağlılığı gözlemlenmiştir. Ayrıca, paramanyetik ve ferromanyetik fazlar arasında kuvvetli etkileşimli ikinci dereceden bir faz geçişi gözlemlenmiştir. Hesaplanan faz diyagramları topolojisinde spin camı ve paramagnetik geri dönüşlere rastlanmıştır. Faz diyagramları ve geçişleri hesaplanırken, Hamiltonyende yer alan etkileşim katsayılarının renormalizasyon grubu dönüşümü altınad gittikleri sabit noktalardan ve sabit dağılımlardan faydalanılmıştır. Tezin ikinci kısmında, fermiyonik Hubbard sistemi üzerinde çalışılarak faz diyagramları ve yoğunluklar hesaplanmıştır. Yoğun, seyrek ve iki ara fazdan oluşan bu sistemde bütün faz geçişlerinin ikinci dereceden olduğu yapılan özdeğer üsteli hesaplamaları sonucunda görülmüştür.
Throughout this thesis, attention was given to phase transitions taking place in classical and quantum systems with specific renormalization-group transformation applications to the Blume-Emery-Griffiths model and the Hubbard model. By calculating the global phase diagram of the Blume-Emery-Griffiths spin-glass model, the phase boundaries in that system were investigated and an inverted tricritical point behavior was observed. Also, a strong-coupling second-order phase transition was observed between the paramagnetic and ferromagnetic phases. In the topologies of the calculated phase diagrams, spin-glass and paramagnetic reentrances were seen. The phase diagrams were determined by the basins of attraction of the renormalization-group sinks, namely the completely stable fixed points and fixed distributions. In the second part of the thesis, the phase diagrams and expectation values were obtained for the fermionic Hubbard model. It was found that the system had four different phases, all of which were separated by second-order phase transitions. The phases found were a dilute phase, a dense phase, and two intermediate phases characterized by enhanced fermion hopping.
Throughout this thesis, attention was given to phase transitions taking place in classical and quantum systems with specific renormalization-group transformation applications to the Blume-Emery-Griffiths model and the Hubbard model. By calculating the global phase diagram of the Blume-Emery-Griffiths spin-glass model, the phase boundaries in that system were investigated and an inverted tricritical point behavior was observed. Also, a strong-coupling second-order phase transition was observed between the paramagnetic and ferromagnetic phases. In the topologies of the calculated phase diagrams, spin-glass and paramagnetic reentrances were seen. The phase diagrams were determined by the basins of attraction of the renormalization-group sinks, namely the completely stable fixed points and fixed distributions. In the second part of the thesis, the phase diagrams and expectation values were obtained for the fermionic Hubbard model. It was found that the system had four different phases, all of which were separated by second-order phase transitions. The phases found were a dilute phase, a dense phase, and two intermediate phases characterized by enhanced fermion hopping.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2008
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2008
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2008
Anahtar kelimeler
Faz Geçişleri,
Renormalizasyon Grubu,
Spin Camları,
BEG Modeli,
Phase Transitions,
Renormalization-Group,
Spin Glass,
BEG Model