Damage spreading in small world Ising models

We study damage spreading in the ferromagnetic Ising model on small world networks using Monte Carlo simulation with Glauber dynamics. The damage spreading temperature T_d is determined as a function of rewiring probability p for small world networks obtained by rewiring the two-dimensional square and three dimensional cubic lattices. We find that the damage for different values of p collapse onto master curves when plotted against a rescaled temperature and that the distance between T_d and the critical temperature T_c increases with p. We argue that when using the Ising model to study social systems, it is necessary to place the spins on a small world network rather than on a regular lattice. © 2002 The American Physical Society.