Dış manyetik alan varlığında dört boyutlu ısıng modelinin creutz 'cellular automaton'ı ile simülasyonu
The simulation of four dimensional ising model in the presence of external magnetic field on the creutz 'cellular automaton'
Yazar: CİHAN KÜRKÇÜ
Danışman: DOÇ. DR. ZİYA MERDAN
Kırıkkale Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Ana Bilim Dalı
Derece: Yüksek Lisans, 2010
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering
Dizin: Creutz hücresel özdevinim = Creutz cellular automation ; Kritik sabitler = Critical exponents

Özet:
Dış manyetik alan varlığında dört boyutlu Ising model L=4, 6, 8 lineer boyutlu sonlu örgüler kullanılarak Creutz ?cellular automaton? ında simüle edildi. h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1 için sonsuz örgünün kritik sıcaklık değerleri, Tc=6.680(1), Tc=6.680(3), Tc=6.691(28), Tc=6.723(15), Tc=6.793(52), Tc=6.938(85), Tc=6.997(62), Tc=7.284(45), Tc=7.797(51), Tc=8.539(3), manyetik alınganlığın maksimumlarının fit değerlerinden elde edildi. h=0, h=0.00025,'da elde edilen düzeltmeli sonsuz örgü kritik sıcaklık değerleri (Tc=6.680(1), Tc=6.680(3)), Seri Açılım (Tc=6.6802, Tc=6.682) (94,95), Monte Carlo (Tc=6.680, Tc=6.6803) (73-95) ve Creutz Cellular Automaton (Tc=6.6800, Tc=6.6700) (44-49) değerleri ile uyumlu olduğu fakat h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1 elde edilen sonsuz örgü kritik sıcaklık değerlerinin (Tc=6.691(28), Tc=6.723(15), Tc=6.793(52), Tc=6.938(85), Tc=6.997(62), Tc=7.284(45), Tc=7.797(51), Tc=8.539(3)) Seri Açılım (Tc=6.6802, Tc=6.682) (94-95), Monte Carlo (Tc=6.680, Tc=6.6803) (73-95) ve Creutz Cellular Automaton (Tc=6.6800, Tc=6.6700) (44-49) değerleri ile uyumlu olmadığı görülmektedir. h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1 için manyetizasyon, manyetik alınganlık ve özısının kritik üsleri beta=0.507(1), beta=0.501(1), beta=0.487(7), beta=0.484(44), beta=0.482(1), beta=0.474(71), beta=0.431(69), beta=0.403(36), beta=0.385(16), beta=0.360(14), gama=1.001(91), gama=1.000(1), gama=0.990(95), gama=0.971(36), gama=0.961(4), gama=0.943(4), gama=0.936(4), gama=0.907(19), gama=0.893(40), gama=0.872(22) ve alfa= -0.015(1), alfa = -0.020(1), alfa = -0.040(1), alfa = -0.040(1), alfa = -0.045(3), alfa = -0.050(4), alfa = -0.060(1), alfa = -0.065(1), alfa = -0.070(1), alfa = -0.070(4) elde edilmiştir. h=0, h=0.00025'da manyetizasyon ve manyetik alınganlık için elde edilen beta=0.507(1), beta=0.501(1) ve gama=1.001(91), gama=1.000(1) kritik üs değerleri beta=1/2 ve gama=1 renormalizasyon grup tahminleri ile uyum halindedir. h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1'da manyetizasyon ve manyetik alınganlık için elde edilen beta=0.487(7), beta=0.484(44), beta=0.482(1), beta=0.474(71), beta=0.431(69), beta=0.403(36), beta=0.385(16), beta=0.360(14) ve gama=0.990(95), gama=0.971(36), gama=0.961(4), gama=0.943(4), gama=0.936(4), gama=0.907(19), gama=0.893(40), gama=0.872(22) kritik üs değerleri beta=1/2 ve gama=1 renormalizasyon grup tahmini ile uyum halinde değildir. h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050 ve h=0.1'da özısı için elde edilen (alfa= -0.015(1), alfa = -0.020(1), alfa = -0.040(1), alfa = -0.040(1), alfa = -0.045(3), alfa = -0.050(4), alfa = -0.060(1), alfa = -0.065(1), alfa = -0.070(1), alfa = -0.070(4)) kritik üs değerleri alfa=0 renormalizasyon grup tahmini ile uyum halindedir.

Abstract:
The four dimensional Ising model in the presence of external magnetic field is simulated on the ?Creutz Cellular Automaton? by using the finite-size lattices with linear dimensions L=4, 6, 8. The values critical temperature of infinite lattice (Tc=6.680(1), Tc=6.680(3), Tc=6.691(28), Tc=6.723(15), Tc=6.793(52), Tc=6.938(85), Tc=6.997(62), Tc=7.284(45), Tc=7.797(51), Tc=8.539(3)) are obtained from the straight line fit of the magnetic susceptibility maxima for h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1, respectively. Although the values obtained of correction infinite lattice critical temperature (Tc=6.680(1), Tc=6.680(3)) are in agreement with series expansion (Tc=6.6802, Tc=6.682) (94,95), Monte Carlo (Tc=6.680, Tc=6.6803) (73-95) and Creutz Cellular Automaton (Tc=6.6800, Tc=6.6700) (44-49) for h=0, h=0.00025, the values obtained of correction infinite lattice critical temperature (Tc=6.691(28), Tc=6.723(15), Tc=6.793(52), Tc=6.938(85), Tc=6.997(62), Tc=7.284(45), Tc=7.797(51), Tc=8.539(3)) aren?t in agreement with series expansion Tc=6.6802, Tc=6.682) (94,95), Monte Carlo (Tc=6.680, Tc=6.6803) (73-95) and Creutz Cellular Automaton (Tc=6.6800, Tc=6.6700) (44-49) for h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1. Critical exponents for the order parameter, the magnetic susceptibility and the specific heat, beta=0.507(1), beta=0.501(1), beta=0.487(7), beta=0.484(44), beta=0.482(1), beta=0.474(71), beta=0.431(69), beta=0.403(36), beta=0.385(16), beta=0.360(14), gama=1.001(91), gama=1.000(1), gama=0.990(95), gama=0.971(36), gama=0.961(4), gama=0.943(4), gama=0.936(4), gama=0.907(19), gama=0.893(40), gama=0.872(22) and alfa= -0.015(1), alfa = -0.020(1), alfa = -0.040(1), alfa = -0.040(1), alfa = -0.045(3), alfa = -0.050(4), alfa = -0.060(1), alfa = -0.065(1), alfa = -0.070(1), alfa = -0.070(4), are obtained for h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1, respectively. The values obtained critical exponents for the order parameter and the magnetic susceptibility (beta=0.507(1), beta=0.501(1) and gama=1.001(91), gama=1.000(1)) are in agreement with the renormalization group prediction of beta=1/2 and gama=1. The values obtained critical exponents for the order parameter and the magnetic susceptibility (beta=0.487(7), beta=0.484(44), beta=0.482(1), beta=0.474(71), beta=0.431(69), beta=0.403(36), beta=0.385(16), beta=0.360(14) and gama=0.990(95), gama=0.971(36), gama=0.961(4), gama=0.943(4), gama=0.936(4), gama=0.907(19), gama=0.893(40), gama=0.872(22)) aren?t in agreement with the renormalization group prediction of beta=1/2 and gama=1 for h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1, respectively. The values obtained critical exponents for specific heat (alfa= -0.015(1), alfa = -0.020(1), alfa = -0.040(1), alfa = -0.040(1), alfa = -0.045(3), alfa = -0.050(4), alfa = -0.060(1), alfa = -0.065(1), alfa = -0.070(1), alfa = -0.070(4)) are in agreement with renormalization group prediction of alfa=0 for h=0, h=0.00025, h=0.00050, h=0.001, h=0.0025, h=0.0050, h=0.01, h=0.025, h=0.050, h=0.1, respectively.