Heriot-Watt Mathematics Report Series
HWM01-29, 27 Jul 2001
Damage spreading in small world Ising models
P Svenson and D Johnston
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.
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