Critical Behavior of the Three-Dimensional Ising model with Anisotropic Bond Randomness at the Ferromagnetic-Paramagnetic Transition Line

We study the $\pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $\pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3d random Ising model. The smooth finite-size behavior of the effective exponents describing the peaks of the logarithmic derivatives of the order parameter provides an accurate estimate of the critical exponent $1/\nu=1.463(3)$ and a collapse analysis of magnetization data gives an estimate $\beta/ \nu=0.516(7)$. These results, are in agreement with previous studies and in particular with those of the isotropic $\pm J$ three-dimensional Ising at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.