Random band matrices are a generalization of Wigner matrices in which matrix elements are concentrated in a band about the diagonal. Spectral properties of these matrices can be expressed in terms of certain statistical mechanics models with hyperbolic symmetry. This talk will discuss a phase transition for a simplified version of one such model in 3D. The model is essentially equivalent to a random walk in a correlated random environment. The transition corresponds to a change in the long time behavior of this walk from localization to diffusion. This is joint work with M. Disertori and M. Zirnbauer.