Universality Class of the Nishimori Point in the 2D $\pm \mathit{J}$ Random-Bond Ising Model

We study the universality class of the Nishimori point in the 2D $\pm J$ random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value $p_c=0.1094\mathrm{}\pm 0.0002$ and estimate $\nu =1.33\mathrm{}\pm 0.03$. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge $c=0.464\mathrm{}\pm 0.004$. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.