Damage spreading in two-dimensional trivalent cellular structures with competing Glauber and Kawasaki dynamics.

The damage spreading of the Ising model on several two-dimensional trivalent structures, including soap froth, Voronoi, and hierarchical structures, are studied with competing Glauber and Kawasaki dynamics. The damage spreading transition temperature T(d) and the Curie temperature T(C) of these structures are compared. We find that T(d) of the hierarchical lattices decreases sharply as the probability of occurrence of Kawasaki dynamics increases, whereas for soap froth and Voronoi, T(d) for the Voronoi and soap froth remain nearly unchanged except when the dynamics is dominated by Kawasaki dynamics. T(d) and T(C) in our two-dimensional structures are nearly the same and they behave similarly as we change the relative probability of occurrence of the Glauber and Kawasaki dynamics. A heuristic argument is provided to explain the numerical results.