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.

23 pages, 12 figs

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