Comments on the critical behavior of random systems

The renormalization-group treatment of the critical behavior of random systems is augmented by including all the cumulants of the disorder distribution. The results substaniate Lubensky's argument that the $n\to 0$ isotropic fixed point is "unphysical," and that the phase transition of random $m$-component systems which have a positive specific-heat exponent will be sharp, with exponents determined by the "random" fixed point. The renormalization-group transformations of a random Gaussian model lead to a "runaway," which is shown to be unrelated to a first-order transition. This is related to the problem of a particle in a random potential with and without an absorptive part.