  The solid-on-solid model is a model of height functions, introduced to study
the interface separating the $+$ and $-$ phase in the Ising model. The planar
solid-on-solid model thus corresponds to the three-dimensional Ising model.
Delocalisation of this model at high temperature and at zero slope was first
derived by Fr\"ohlich and Spencer, in parallel to proving the
Kosterlitz-Thouless phase transition. The first main result of this article
consists of a simple, alternative proof for delocalisation of the
solid-on-solid model. In fact, the argument is more general: it works on any
planar graph -- not just the square lattice -- and implies that the interface
delocalises at any slope rather than exclusively at the zero slope. The second
main result is that the absolute value of the height function in this model
satisfies the FKG lattice condition. This property is believed to be intimately
linked to the (quantitative) understanding of delocalisation, given the recent
successes in the context of the square ice and (more generally) the six-vertex
model. The new FKG inequality is shown to hold true for both the solid-on-solid
model as well as for the discrete Gaussian model, which implies immediately
that the two notions of delocalisation, namely delocalisation in finite volume
and delocalisation of shift-invariant Gibbs measures, coincide.
