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

## TL;DR

This study investigates the critical behavior of the 3D ±J Ising model along the ferromagnetic transition line, providing numerical evidence that it shares the same universality class as the 3D randomly-dilute Ising model, with consistent critical exponents.

## Contribution

The paper demonstrates through finite-size scaling and Monte Carlo simulations that the ferromagnetic transition line of the 3D ±J Ising model belongs to the same universality class as the randomly-dilute Ising model, with precise critical exponent estimates.

## Key findings

- Critical exponents ν=0.682(3) and η=0.036(2) are obtained.
- Critical behavior along the transition line matches that of the randomly-dilute Ising universality class.
- Numerical evidence supports universality across the transition line from p=1 to the Nishimori point.

## 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.