Damage spreading in small world Ising models

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We study damage-spreading in the ferromagnetic Ising model on small world networks using Monte Carlo simulation with Glauber dynamics. The damage spreading temperature Td is determined as a function of rewiring probability p for small world networks obtained by rewiring the 2D square and 3D 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 Td and the critical temperature Tc 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.