Global random-field spin-glass phase diagrams in two and three dimensions

An Ising model including field randomness and $\pm J$ bond randomness is studied by renormalization-group theory in spatial dimensions $d=2\mathrm{}$ and 3. In $d=3,$ with field randomness but no $\pm J$ randomness, ferromagnetic and paramagnetic phases occur with no intervening spin-glass phase. Also in $d=3,$ at sufficient $\pm J$ randomness, a spin-glass phase occurs, but is replaced by the paramagnetic phase for any nonzero random field, also implying its disappearance for any nonzero uniform field. In $d=2,$ no ferromagnetic phase under random fields and no spin-glass phase occur. Global phase diagrams uniting the random-field and spin-glass problems are evaluated. The strong violation of critical phenomena universality, previously found adjoining random-bond tricriticality in $d=3,$ is seen here in $d=2.\mathrm{}$