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Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model

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.