Exact recovery in block spin Ising models at the critical line

@article{Lowe2019ExactRI,
  title={Exact recovery in block spin Ising models at the critical line},
  author={Matthias Lowe and Kristina Schubert},
  journal={arXiv: Probability},
  year={2019}
}
We show how to exactly reconstruct the block structure at the critical line in the so-called Ising block model. This model was re-introduced by Berthet, Rigollet and Srivastava in a recent paper. There the authors show how to exactly reconstruct blocks away from the critical line and they give an upper and a lower bound on the number of observations one needs; thereby they establish a minimax optimal rate (up to constants). Our technique relies on a combination of their methods with fluctuation… 
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Cutoff and Dynamical Phase Transition for the General Multi-component Ising Model
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