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

The Random-Bond Ising Model in 2.01 and 3 Dimensions