Critical and multicritical behavior of the ±J Ising model in two and three dimensions

We report our Monte Carlo results on the critical and multicritical behavior of the ±J Ising model [with a random-exchange probability P (Jxy) = pδ(Jxy−J)+(1−p)δ(Jxy +J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p = 1 to a multicritical (Nishimori) point. By a finitesize scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.