  We consider replicated $O(N)$ symmetry in two dimensions within the exact
framework of scale invariant scattering theory and determine the lines of
renormalization group fixed points in the limit of zero replicas corresponding
to quenched disorder. A global pattern emerges in which the different critical
lines are located within the same parameter space. Within the subspace
corresponding to the pure case (no disorder) we show how the critical lines for
non-intersecting loops ($-2\leq N\leq 2$) are connected to the zero temperature
critical line ($N>2$) via the BKT line at $N=2$. Disorder introduces two more
parameters, one of which vanishes in the pure limit and is maximal for the
solutions corresponding to Nishimori-like and zero temperature critical lines.
Emergent superuniversality (i.e. $N$-independence) of some critical exponents
in the disordered case and disorder driven renormalization group flows are also
discussed.
