The simulation of the phase transitions of the three dimensional blume-emery-griffiths model on a cellular automaton

vTHE SIMULATION OF THE PHASE TRANSITIONS OF THE THREE-DIMENSIONAL BLUME-EMERY-GRIFFITHS MODEL ON A CELLULARAUTOMATON(Ph.D Thesis)Nurgül SEFEROĞLUGAZI UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYJanuary 2007ABSTRACTIn this study, Blume-Emery-Griffiths model with the ferromagneticbilinear interaction is simulated using the heating algorithm which isimproved from the Creutz cellular automaton. The simulations havebeen made in the − 3 < D / J < 3 and − 2 ≤ K / J ≤ 0 parameter regions on asimple cubic lattices with linear dimensions L=12, 16, 18 and 24. Thetemperature variations of the thermodynamic quantities and theprobability distribution of the order parameter (P(m)) are investigated toobtain the phase diagrams of the model. The calculations show that themodel exhibits the re-entrant and double re-entrant phase transitionsfor certain values of D/J and K/J parameters near the phase boundary.In addition, the static critical exponents (ν, β, γ and α) are estimated byanalyzing the data within the framework of finite-size scaling theory. Itis obtained that 3-d BEG model exhibits the universality behavior of thethree-dimensional Ising model for all the continuous transition.Science Code : 202.1.147Keywords : Blume-Emery-Griffiths(BEG) model, Creutz cellularautomaton, Re-entrant phase transition, 3-d.Page Number : 103Adviser : Prof. Dr. Bülent KUTLU