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

Abstract

In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $\hat{I}{»}_w=\log (\frac{1}{1-e^{-4{\hat{I}}^2}})$. At $\hat{I}»<\hat{I}{»}_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac{1}{4{\hat{I}}^2}\log n+O(1)$; at $\hat{I}»>\hat{I}{»}_w$ it is localized at some $O(1)$ height. We show that at $\hat{I}»=\hat{I}{»}_w$, there is delocalization, with rigidity now at height $\lfloor \frac{1}{6{\hat{I}}^2}\log n+\frac{1}{3}\rfloor$, confirming a conjecture of Lacoin.

12 pages