  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.
