Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

@article{Gheissari2017ZeroTemperatureDI,
  title={Zero-Temperature Dynamics in the Dilute Curie–Weiss Model},
  author={Reza Gheissari and Charles M. Newman and Daniel L. Stein},
  journal={Journal of Statistical Physics},
  year={2017},
  volume={172},
  pages={1009-1028}
}
We consider the Ising model on a dense Erdős–Rényi random graph, $${\mathcal {G}}(N,p)$$G(N,p), with $$p>0$$p>0 fixed—equivalently, a disordered Curie–Weiss Ising model with $$\hbox {Ber}(p)$$Ber(p) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the… Expand
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