By mapping the Edwards-Anderson model onto a nonrandom Ising model we argue that the lower critical dimension
d∗ for the Edwards-Anderson spin-glass is close to 3 and may depend on the probability distribution of the bond strengths. For
d>d∗, the approach to spin-glass order from the paramagnetic phase is characterized by Ising exponents. At
d=d∗, however, the critical exponents defined for
T>Tc are twice the corresponding Ising ones. These results are consistent with recent computer simulations.
We study the superfluid-insulator transition of a particle-hole symmetric system of long-range interacting bosons in a time-dependent random potential in two dimensions, using the momentum-shell renormalization-group method. We find a stable fixed point with nonzero values of the parameters representing the short- and long-range interactions and disorder when the interaction is asymptotically logarithmic. This is contrasted to the nonrandom case with a logarithmic interaction, where the transition is argued to be first order, and to the
1/r Coulomb interaction case, where either a first-order transition or an
XY-like transition is possible depending on the parameters. We propose that our model may be relevant in studying the vortex liquid-vortex glass transition of interacting vortex lines in point-disordered type-II superconductors.