  We examine the ground state of the random quantum Ising model in a transverse
field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG)
scheme. For spatial dimensionality d=2, we find that at strong randomness the
RG flow for the quantum critical point is towards an infinite-randomness fixed
point, as in one-dimension. This is consistent with the results of a recent
quantum Monte Carlo study by Pich, et al., including estimates of the critical
exponents from our RG that agree well with those from the quantum Monte Carlo.
The same qualitative behavior appears to occur for three-dimensions; we have
not yet been able to determine whether or not it persists to arbitrarily high
d. Some consequences of the infinite-randomness fixed point for the quantum
critical scaling behavior are discussed. Because frustration is irrelevant in
the infinite-randomness limit, the same fixed point should govern both
ferromagnetic and spin-glass quantum critical points. This RG maps the random
quantum Ising model with strong disorder onto a novel type of
percolation/aggregation process.
