Critical wetting in the (2+1)D Solid-On-Solid model

In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential λw= log (11-e-4β). At λ<λw entropic repulsion causes the surface to delocalize and be rigid at height 14βlog n+O(1); at λ>λw it is localized at some $O(1)$ height. We show that at λ=λw, there is delocalization, with rigidity now at height 16βlog n+13, confirming a conjecture of Lacoin.