Intermediate coupling phase diagrams of the cuprates*

We analyze the competing (non-superconducting) phases in the cuprates in the intermediate coupling regime via Gutzwiller approximation (GA) + RPA. The magnetic GA+RPA phase diagram was benchmarked for the $t-t'-U$ model[1]. The leading instabilities are associated with Fermi surface nesting, generally corresponding to a double nesting criterion, and are different for different cuprates. While electron-doped cuprates are generally associated with commensurate $(\pi ,\pi )$ nesting [2], there are competing incommensurate phases in the hole doped cuprates. Magnetic and charge-order phase diagrams will be compared. [1] L.F. Tocchio, {\it et al.}, Phys. Rev. B{\bf 78}, 041101(R) (2008). [2] C. Kusko, {\it et al.}, Phys. Rev. B. {\bf{66}}, 140513(R) (2002); T. Das, {\it et al.}, Phys. Rev. Lett. {\bf{98}}, 197004 (2007).