Quantitative delocalization for solid-on-solid models at high temperature and arbitrary tilt

TL;DR

This paper proves that at high temperature, a class of 2D integer-valued interface models, including solid-on-solid and p-SOS models, exhibit logarithmic delocalization regardless of boundary conditions, using an improved multi-scale approach.

Contribution

It extends previous work by Fr"ohlich and Spencer to arbitrary boundary data and provides technical improvements in the multi-scale proof technique.

Findings

Interface models are delocalized at high temperature

Delocalization is logarithmic and boundary data independent

The proof employs an improved multi-scale argument

Abstract

We study a family of integer-valued random interface models on the two-dimensional square lattice that include the solid-on-solid model and more generally $p$-SOS models for $0<p\le2$, and prove that at sufficiently high temperature the interface is delocalized logarithmically uniformly in the boundary data. Fr\"ohlich and Spencer had studied the analogous problem with free boundary data, and our proof is based on their multi-scale argument, with various technical improvements.