The 3D +-J Ising model at the ferromagnetic transition line

Abstract

We study the critical behavior of the three-dimensional $\pm J$ Ising model [with a random-exchange probability $P(J_{xy}) = p \delta(J_{xy} - J) + (1-p) \delta(J_{xy} + J)$] at the transition line between the paramagnetic and ferromagnetic phase, which extends from $p=1$ to a multicritical (Nishimori) point at $p=p_N\approx 0.767$. By a finite-size scaling analysis of Monte Carlo simulations at various values of $p$ in the region $p_N<p<1$, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensional randomly-dilute Ising model. We obtain the results $\nu=0.682(3)$ and $\eta=0.036(2)$ for the critical exponents, which are consistent with the estimates $\nu=0.683(2)$ and $\eta=0.036(1)$ at the transition of randomly-dilute Ising models.