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

Abstract

We study the phase diagram and critical properties of the two-dimensional disordered O(n) loop model. The renormalization group (RG) flow is extracted from the landscape of the effective central charge c obtained by the transfer matrix method. We find a line of multicritical fixed points (FPs) at strong randomness for n > nc ∼ 0.5. We also find a line of stable random FPs for nc < n < 1, whose c and critical exponents agree well with the 1 − n expansion results. The multicritical FP at n = 1 has c = 0.4612(4), which suggests that it belongs to the universality class of the Nishimori point in the 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 .