Nonuniversality in random criticality

We consider N two-dimensional Ising models coupled in the presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of N other than 1. We show how this result relates to perturbative studies and sheds light on numerical simulations. We also observe that the limit N -> 1 may be of interest for the Ising spin glass, and point out the potential relevance for nonuniversality in other contexts of random criticality.