In the Wikipedia entry associated with the Kahn-Kalai conjecture, there is the following assertion
This conjecture concerns the general problem of estimating when phase transitions occur in systems.
As this entry notes, the conjecture (technically "theorem", as is recently proved) is
in the field of graph theory and statistical mechanics
I am particularly interested in the consequences of this conjecture in view of statistical mechanics and (even if possible) its implications and applications to formation of complex networks in engineering fields. The main article, as far as I can see, heavily focuses on graph-theoretic facets of the conjecture. So, is there any applied exposition of this conjecture?