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In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d=3 and 2 are studied. With the removal of just 51 % of frustration, a spin-glass phase occurs in d=2. With the addition of just 33 % frustration, the spin-glass phase disappears in d=3. Sequences of 18 different phase diagrams for different levels of frustration are calculated in both dimensions. In general, frustration lowers the spin-glass ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. Chaos increases with increasing frustration, as seen from the increased positive value of the calculated Lyapunov exponent $lambda$, starting from $lambda =0$ when frustration is absent. The calculated runaway exponent $y_R$ of the renormalization-group flows decreases with increasing frustration to $y_R=0$ when the spin-glass phase disappears. From our calculations of entropy and specific heat curves in d=3, it is seen that frustration lowers in temperature the onset of both long- and short-range order in spin-glass phases, but is more effective on the former. From calculations of the entropy as a function of antiferromagnetic bond concentration p, it is seen that the ground-state and low-temperature entropy already mostly sets in within the ferromagnetic and antiferromagnetic phases, before the spin-glass phase is reached.
All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found th
We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a shor
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration
The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase dia
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