Commentary to: Oriented Percolation in One-Dimension 1/|x−y|2 Percolation Models

@article{Marchetti2013CommentaryTO,
  title={Commentary to: Oriented Percolation in One-Dimension 1/|x−y|2 Percolation Models},
  author={Domingos H. U. Marchetti and Vladas Sidoravicius and Maria Eulalia Vares},
  journal={Journal of Statistical Physics},
  year={2013},
  volume={150},
  pages={804-805}
}
The main result of the article (Theorem 1.1) is the occurrence of oriented percolation for the independent edge percolation model on Z, with occupation probabilities p{x,y} = 1 − exp(−β/|x − y|2) if |x − y| > 1 and p{x,x+1} = p, for β > 1 and p sufficiently close to one. Together with FKG inequalities this has implications for the Ising model, as stated in Corollary 1.2. It should be added that the content of Corollary 1.2 is an immediate consequence of Theorem 3.4, Sect. 3(ii) in [1], with the… 
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A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

References

An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation, Ising and Potts models

We rigorously establish the existence of an intermediate ordered phase in one-dimensional 1/|x−y|2 percolation, Ising and Potts models. The Ising model truncated two-point function has a power law