Commentary to: J Stat Phys (2010) 139:941–959 DOI 10.1007/s10955-010-9966-z

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 result holding even for β>1. This fact was missed by the authors at the time the article was written.

We take the opportunity for adding a minor correction: at Remark 1, following Theorem 1.1, instead of “β replaced by β′≥κβ.” one should read “β replaced by β′≥κβ and p similarly replaced by p′=1−(1−p)β′/β.” (That is, writing p=1−e −βJ in the first line of (1.1) we replace β by β′.)