  We study gradient models on the lattice $\mathbb{Z}^d$ with non-convex
interactions. These Gibbs fields (lattice models with continuous spin) emerge
in various branches of physics and mathematics. In quantum field theory they
appear as massless field theories. Even though our motivation stems from
considering vector valued fields as displacements for atoms of crystal
structures and the study of the Cauchy-Born rule for these models, our
attention here is mostly devoted to interfaces, with the gradient field as an
\emph{effective} interface interaction. In this case we prove the strict
convexity of the surface tension (interface free energy) for low temperatures
and sufficiently small interface tilts using muli-scale (renormalisation group
analysis) techniques following the approach of Brydges and coworkers
\cite{B07}. This is a complement to the study of the high temperature regime in
\cite{CDM09} and it is an extension of Funaki and Spohn's result \cite{FS97}
valid for strictly convex interactions.
