Comments on Disordered Conformal Field Theories

We consider Conformal Field Theories perturbed by quenched disorder. Such systems often flow to
+new, disordered, fixed points of the
renormalization group. For the Ising model in d = 3 with random bonds, we calculate
some properties of the disordered fixed point in perturbation theory in the heat capacity
exponent. Our results are consistent with experimental data. We further analyze several
aspects of large-N disordered theories. A natural large-N limit of theories with disorder
is identied. We find a nontrivial generalization of the Imry-Ma instability. The beta
functions at large N can be computed exactly. The presence of double trace operators
changes the heat capacity exponent expansion in a qualitative fashion. We solve a class of
disordered large-N theories and find the new critical exponents.