Zero temperature Glauber dynamics on complex networks

Abstract

We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power-law degreedistribution. Application of mean-field theory yields as main prediction that for symmetric disordered initial conditions the mean time to reach full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate to describe this problem.

20 pages, 10 figures

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• Dynamics-Driven Evolution to Structural Heterogeneity in Complex Networks
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• Absorbing states of zero-temperature Glauber dynamics in random networks
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• Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices
• Optimized brute-force algorithms for the bifurcation analysis of a spin-glass-like neural network model
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• Scalar model of flocking dynamics on complex social networks
• Influence of distinct kinds of temporal disorder in discontinuous phase transitions
• Disordered configurations of the Glauber model in two-dimensional networks
• Flocking dynamics mediated by weighted social networks