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 ${\mathit{\lambda }}_w=log(\frac{1}{1-e^{-4\mathit{\beta }}})$. At $\mathit{\lambda }<{\mathit{\lambda }}_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac{1}{4\mathit{\beta }}logn+O(1)$; at $\mathit{\lambda }>{\mathit{\lambda }}_w$ it is localized at some $O(1)$ height. We show that at $\mathit{\lambda }={\mathit{\lambda }}_w$, there is delocalization, with rigidity now at height $\lfloor \frac{1}{6\mathit{\beta }}logn+\frac{1}{3}\rfloor$, confirming a conjecture of Lacoin.