Damage spreading in small world Ising models

Abstract

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 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 $T_d$ 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.