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

TL;DR

This paper investigates the critical wetting transition in a (2+1)D Solid-On-Solid model, revealing a precise height scaling at the critical point and confirming a theoretical conjecture about interface delocalization.

Contribution

It provides a rigorous analysis of the critical wetting transition in the (2+1)D SOS model, including exact height scaling at the critical pinning potential, confirming Lacoin's conjecture.

Findings

Delocalization at subcritical potential with height ~ (1/4β) log n

Localization at supercritical potential with O(1) height

Critical point exhibits a distinct height scaling of ~ (1/6β) log n

Abstract

In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $\lambda_w= \log (\frac{1}{1-e^{-4\beta}})$. At $\lambda<\lambda_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac1{4\beta}\log n+O(1)$; at $\lambda>\lambda_w$ it is localized at some $O(1)$ height. We show that at $\lambda=\lambda_w$, there is delocalization, with rigidity now at height $\lfloor \frac1{6\beta}\log n+\frac13\rfloor$, confirming a conjecture of Lacoin.