Dış manyetik alan varlığında dört boyutlu ısıng modelinin creutz `cellular automaton`ı ile simülasyonu

Abstract

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.

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.