Ising model on two-community SBM undergoes uniqueness/non-uniqueness transition almost surely, with magnetization converging to 2- or 4-point Dirac mixtures in supercritical regime and quenched CLT in subcritical uniqueness region.
On the Effect of Bottlenecks in Block Spin Models
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abstract
We study a bottleneck spin model with $N$ spins, split into two Curie-Weiss models at low temperature with a bottleneck between them. We propose multiple ways of how to realize such a bottleneck and study its influence on the phase transition in the thermodynamic limit $N \to \infty$. In all versions of this model we prove the existence of a threshold that determines whether or not the presence of the bottleneck is felt in the phase transition. This threshold depends on the size of the bottleneck and the interaction strength through it.
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The Ising Model on a Two-Community Stochastic Block Model
Ising model on two-community SBM undergoes uniqueness/non-uniqueness transition almost surely, with magnetization converging to 2- or 4-point Dirac mixtures in supercritical regime and quenched CLT in subcritical uniqueness region.