Negative scaling dimensions and conformal invariance at the Nishimori point in the±Jrandom-bond Ising model

Abstract

We reexamine the disorder-dominated multicritical point of the two-dimensional $\ifmmode\pm\else\textpm\fi{}J$-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 $q\mathrm{th}$ 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 multiscaling 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.