Study of two dimensional Ising model using creutz cellular automaton

STUDY OF TWO DIMENSIONAL ISING MODEL USING CREUTZ CELLULAR AUTOMATON Ph. D. Thesis Bülent KUTLU GAZÎ UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY April 1995 ABSTRACT The critical exponents for two dimensional Ising model are computed on Creutz cellular automaton. The data are analyzed according to the finite-size scaling theory. The values of the static critical exponents a=0.04, {3= 0.13, y =1.77, v=1.01, iy=0.24, and y=1.02, which are related to the specific heat, the order parameter, the susceptibility, the correlation length, the correlation function, and the interfacial tension, are in good agreement with their well- established values. The values of the linear dynamical critical exponents A A n A zE=zM=2.20, zE=0.19 and zM=1.91 which are computed from the relaxations of the time-displaced correlation and autocorrelation functions for the internal energy and the order parameter at the critical temperature, and the values of the nonlinear dynamical critical exponents zE°=1.05 and zM = 2.07 which are obtained from the nonlinear relaxations of the internal energy and the order parameter near the critical temperature, agree with the results of various other methods. These values for static and dynamical critical exponents verify the scaling relations among them. Science Code : 404.01.01 Key Words : Ising model, cellular automata, finite-size scaling theory, critical exponents Page : 124 Supervisor :Prof. Dr. Nevzat Aktekin TIT