We study the two-dimensional O(n) symmetric loop model with quenched bond randomness. The phase diagram comprises a mixture of weak-coupling (perturbative) and strong-coupling (non-perturbative) critical fixed points, leading to a physics that differs in several ways from that of the better studied random-bond Q-state Potts model. A perturbative expansion around the Ising limit (n=1 or Q=2) is possible in both models, but the results are dissimilar due to the different identifications of the energy operator. Moreover, the line of random fixed points in the O(n) model continues into a strong-coupling branch whose continuum limit we identify as an O(n) symmetric deformation of the Nishimori point in the +-J Ising spin glass. For n $>>$ 2 the model can be related to a random-field three-state Potts model.

LPT, ENS and Univ. Paris 6