  We consider the Ising model between 2 and 4 dimensions perturbed by quenched
disorder in the strength of the interaction between nearby spins. In the
interval 2<d<4 this disorder is a relevant perturbation that drives the system
to a new fixed point of the renormalization group. At d=2 such disorder is
marginally irrelevant and can be studied using conformal perturbation theory.
Combining conformal perturbation theory with recent results from the conformal
bootstrap we compute some scaling exponents in an expansion around d=2. If one
trusts these computations also in d=3, one finds results consistent with
experimental data and Monte Carlo simulations. In addition, we perform a direct
uncontrolled computation in d=3 using new results for low-lying operator
dimensions and OPE coefficients in the 3d Ising model. We compare these new
methods with previous studies. Finally, we comment about the $O(2)$ model in
d=3, where we predict a large logarithmic correction to the infrared scaling of
disorder.
