Study of eight-dimensional ısıng model using (4)8-4 lattices on the Creutz cellular automaton

In this work, the eight-dimensional Ising model is simulated on the Creutz cellular automaton. Simulations are carried out on the simple hypercubic lattices Ü of linear dimension L=4 with periodic boundary conditions and using four binary bit demons near the critical temperature of the finite size lattice. The values of specific heat order parameter and magnetic susceptibility computed are averages over the lattices and the number of time steps (60 000, 120 000, 180 000) during which the cellular automaton develops. The values of critical temperature for the specific heat and the magnetic susceptibility are Tc= 14,7904 ±0,0004; Tc =14,7905 ±0,0009 ; Tc =14,7904 ±0,0004 and Tc= 14,8240 ±0,0028; Tc =14,8252 ±0,0011; Tc =14,8253 ±0,0005, respectively. The values of critical exponent for the magnetic susceptibility and the order parameter are computed using the values of critical temperature for the magnetic susceptibility. These values are in agreement with the renormalization group prediction (p = p' = 0,5; y = y ' = 1 ) and with other teoric values ( p = p' = 0,48 ; y = y' = 1,05 ).VI Bilim Kodu : 228 Anahtar Kelimeler : Ising Model, Creutz Cellular Automaton, Critical Exponents Sayfa Adedi : 59 Tez Yöneticisi : Prof. Dr. Abdullah GÜNEN