The Damage Spreading For The Ising And Potts Models On Two-dimensional Triangle Lattices

The damage spreading for the Ising and Potts models ontwo-dimensional triangle lattices is studied in this paper.The damage spreading on two-dimensional Small World Networks(SWN) under the mixed Glauber and Kawasaki dynamics is studied withIsing model and using Monte Carlo method. The variations of criticalphase transition temperature with various possibilities of SWN as well asof clustering coefficient with possibility of SWN are also discussed. It isshown that the phase transition temperature increases with the possibilityof SWN if Glauber dynamics is dominate, but if the Kawasaki dynamicsis dominating, the damage tends to be happened without phase transitionregardless of the possibility of SWN obtained. The damage spreading isaffected by both dynamic and the function of SWN. The bigger thepossibility of SWN becomes, the more difficult the damage spreads. Thereason is that the damage spreading is determined by the cells with thebiggest edge number. The result of simulation shows that the clusteringcoefficient in the model is inversely proportion to the possibility of SWN.The Diluted-Ising model and Potts model are studied under Glauberdynamic. The relation of the possibility of dilution and the damagespreading is discussed on the Diluted-Ising model. It is shown that thedamage spreading is lower than 0.5 when the possibility of dilution ishigher than a certain value. If there are too many isolated points on thelattice, the damage spreading is frozen on the original state. With thepossibility of dilution increasing, the phase transition temperaturedecreases. In addition, the clustering coefficients are calculated as thefunction of the possibility of dilution and they are consistent with the former research results. For the Potts model, the phase transitiontemperatures are obtained for 2＜q＜9. The result of comparing withsquare lattice Potts model and the triangle Ising model shows that thetrivalent Potts model has more superiority than others on restraining thedamage spreading.