We consider models of gradient type, which is the density 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-cancave 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 ergodic infinite volume Gibbs measure with mean zero for the potential $$V$$ above scales to a Gaussian free field.