  An elementary Ising spin model is proposed for demonstrating cascading
failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in
realistic networks for distribution and delivery by suppliers to consumers. A
ferromagnetic Hamiltonian with quenched random fields results from policies
that maximize the gap between demand and delivery. Such policies can arise in a
competitive market where firms artificially create new demand, or in a solidary
environment where too high a demand cannot reasonably be met. Network failure
in the context of a policy of solidarity is possible when an initially active
state becomes metastable and decays to a stable inactive state. We explore the
characteristics of the demand and delivery, as well as the topological
properties, which make the distribution network susceptible of failure. An
effective temperature is defined, which governs the strength of the activity
fluctuations which can induce a collapse. Numerical results, obtained by Monte
Carlo simulations of the model on (mainly) scale-free networks, are
supplemented with analytic mean-field approximations to the geometrical random
field fluctuations and the thermal spin fluctuations. The role of hubs versus
poorly connected nodes in initiating the breakdown of network activity is
illustrated and related to model parameters.
