Cellular Automata-based Optimization of the Spin-Glass Discrete Problem in a Ferromagnetic.pdf

Appl. Math. Inf. Sci. 6-3S, 829-835 (2012) 829 Cellular Automata-based Optimization of the Spin-Glass Discrete Problem in a Ferromagnetic and Anti- ferromagnetic Material Jianjia He and Fuyuan Xu Business School, University of Shanghai for Science and Technology, Shanghai 200093, P.R. China Center for Supernetworks Research (China), University of Shanghai for Science and Technology, Shanghai, China Email: xufy@usst.edu.cn Accepted 03 Aug. 2012; Published online: 17 Nov. 2012 Abstract: According to the discussion about the discrete characters of Spin glass on Ising model, the feasibility to study spin glass based on cellular automata is demonstrated, while a method searching for lower energy state of the spin glass based on Cellular Automata is proposed. This method achieves energy optimization of the material and calculate the total energy of the system by programming the cellular automata with Visual C + + and using the Ising model and the Neumann’s defining for neighbor node. Among the experiment of cold compress spin, the natural optimization process of energy can be simulated. When the temperature is higher than Curie point, the internal magnetic field of ferromagnetic materials is in a state of disorder and becomes a paramagnet. This phase change is reversible in nature. While the magnetic field of anti-ferromagnetic materials tends to be empty with the temperature decreasing. The result shows that cellular automata is much more superior compared with simulated annealing algorithm, which may not only introduce a new way to study magnetic Spin glass, but also explore other optimization problems, such as the ground state problem of SDN, TSP, peddler problem, satisfiability problem and so on. Keywords: Cellular Automata; Spin-Glass; Ising Model; Local Optimization; Simulated Annealing Algorithm 1 INTRODUCTION This paper discusses a simulation algorithm--cellular