  We numerically study the phase diagram and critical properties of the
two-dimensional disordered O(n) loop model by using the transfer matrix and the
worm Monte Carlo methods. The renormalization group flow is extracted from the
landscape of the effective central charge obtained by the transfer matrix
method based on the Zamolodchikov's C-theorem. We find a line of random fixed
points (FPs) for $n_c < n <1$, with $n_c \sim 0.5$, for which the central
charge and critical exponents agree well with the results of the $1-n$
perturbative expansion. Furthermore, for $n> n_c$, we find a line of
multicritical FPs at strong randomness. The FP at $n=1$ has $c=0.4612(4)$,
which suggests that it belongs to the universality class of the Nishimori point
in the $\pm J$ random-bond Ising model. For $n>2$, we find another critical
line that connects the hard-hexagon FP in the pure model to a finite-randomness
zero-temperature FP.
