We consider models of gradient type, which are the densities of a collection of real-valued random variables $φ:=\{φ_x: x \in Λ\}$ given by $Z^{-1}\exp({-\sum\nolimits_{j \sim k}V(φ_j-φ_k)})$. We focus our study on the case that $V(\nablaφ) = [1+(\nablaφ)^2]^α$ with $0 < α< 1/2$, 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 $\left<[v \cdot φ]^p \right>$ 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.