  We consider gradient models on the lattice $\mathbb{Z}^d$. These models serve
as effective models for interfaces and are also known as continuous Ising
models. The height of the interface is modelled by a random field with an
energy which is a non-convex perturbation of the quadratic interaction. We are
interested in the Gibbs measure with tilted boundary condition $u$ at inverse
temperature $\beta$ of this model. In [AKM16], [Hil16] and [ABKM19] the authors
show that for small tilt $u$ and large inverse temperature $\beta$ the surface
tension is strictly convex, where the limit is taken on a subsequence.
Moreover, it is shown that the scaling limit (again on a subsequence) is the
Gaussian free field on the continuum torus. The method of the proof is a
rigorous implementation of the renormalisation group method following a general
strategy developed by Brydges and coworkers.
  In this paper the renormalisation group analysis is extended from the
finite-volume flow to an infinite-volume version to eliminate the necessity of
the subsequence in the results in [AKM16], [Hil16] and [ABKM19].
