  We consider models of gradient type, which are the densities of a collection
of real-valued random variables $\phi :=\{\phi_x: x \in \Lambda\}$ given by
$Z^{-1}\exp({-\sum\nolimits_{j \sim k}V(\phi_j-\phi_k)})$. We focus our study
on the case that $V(\nabla\phi) = [1+(\nabla\phi)^2]^\alpha$ with $0 < \alpha <
1/2$, which is a non-convex potential. We introduce an auxiliary field $t_{jk}$
for each edge and represent the model as the marginal of a model with
log-concave density. Based on this method, we prove that finite moments of the
fields $\left<[v \cdot \phi]^p \right>$ are bounded uniformly in the volume.
This leads to the existence of infinite volume measures. Also, every
translation invariant, ergodic infinite volume Gibbs measure for the potential
$V$ above scales to a Gaussian free field.
