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Negative scaling dimensions and conformal invariance at the Nishimori point in the +/-J random-bond Ising model

We reexamine the disorder-dominated multicritical point of the two-dimensional +/-J Ising model, known as the Nishimori point (NP). At the NP we investigate numerically and analytically the behavior of the disorder correlator, familiar from the self-dual description of the pure critical point of the two-dimensional Ising model. We consider the logarithmic average and the q-th moments of this correlator in the ensemble average over randomness, for continuous q in the range 0<q<2.5, and demonstrate their conformal invariance. At the NP we find, in contrast to the self-dual pure critical point, that the disorder correlators exhibit multi-scaling in q which is different from that of spin-spin correlators and that their scaling dimension becomes negative for q>1 and q<0. Using properties on the Nishimori line we show that the first moment (q=1) of the disorder correlator is exactly one for all separations. The spectrum of scaling dimensions at the NP is not parabolic in q.