Scaling of connected spin avalanches in growing networks

Abstract

We use the damage spreading method to investigate the spectra of connected spin avalanches in the exponential networks and the scale-free networks with antiferromagnetically coupled spins. The results suggest that the avalanche spectra are characterized by the same statistics as the degree distribution in their home networks. Further, the obtained mean range Z of an avalanche, i.e., the maximal distance reached by an avalanche from the damaged site, scales with the avalanche size s as Z/N β=f(s/N α), where α=0.5 and β=0.33. These values are true for both kinds of networks for the number M of nodes to which new nodes are attached between 4 and 10; a check for M=25 confirms these values as well.

Damage spreading in a driven lattice gas model

“…Damage spreading studies were originally applied to the Ising model, spin glasses and cellular automata, but they have also been applied to magnetic systems such as the Potts model with q-states, Heisenberg and XY models, two-dimensional trivalent cellular structures, biological evolution, non-equilibrium models, opinion dynamics, and small world networks (see e.g. [23] and references therein, and for more recent results see [18,24,25,26,27,28,29,30]).…”

Gardens of Eden in systems of bistable nanoscopic wires

“…could a local damage spread without limits? If the answer is positive, an intriguing property of the probability distributions of such avalanches of this kind is their universal scale-free character [19]. However, the averaging over spatially disordered ensembles of wires is very time-consuming.…”

Phase transitions and damage spreading in a nonequilibrium lattice gas model with mixed dynamic rules

“…[17] and references therein, and for more recent results see Refs. [12,[18][19][20][21][22][23][24][25][26][27]).…”