The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges o
f temperatures, electron densities, and further/first-neighbor interaction strength ratios. In addition to the tau_{tJ} phase seen in earlier studies of the nearest-neighbor d=3 tJ model, the tau_{Hb} phase seen before in the d=3 Hubbard model appears both near and away from half-filling. These distinct tau phases potentially correspond to different (BEC-like and BCS-like) superconducting phases.
For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire rang
e of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.
The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d geq 3. The asymmetry
at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding to the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d geq 6, resulting in a new multicritical point at its meeting with the boundaries to the paramagnetic phase. In d=3,4,5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.
