Zero-temperature Glauber dynamics on small-world networks

Abstract

The zero-temperature Glauber dynamics of the ferromagnetic Ising model on small-world networks, rewired from a two-dimensional square lattice, has been studied by numerical simulations. For increasing disorder in finite networks, the nonequilibrium dynamics becomes faster, so that the ground state is found more likely. For any finite value of the rewiring probability p, the likelihood of reaching the ground state goes to zero in the thermodynamic limit, similarly to random networks. The spin correlation xi(r) is found to decrease with distance as xi(r) ~ exp(-r/lambda), lambda being a correlation length scaling with p as lambda ~ p^(-0.73). These results are compared with those obtained earlier for addition-type small world networks.

8 pages, 9 figures

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• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Ising model in clustered scale-free networks
• Absorbing states of zero-temperature Glauber dynamics in random networks
• Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices
• Disordered configurations of the Glauber model in two-dimensional networks