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

TL;DR

This study investigates the critical behavior of an anisotropic 3D Ising model with bond randomness, finding it belongs to the same universality class as the isotropic case and estimating critical exponents with high precision.

Contribution

It provides the first detailed numerical analysis of the anisotropic 3D random Ising model at the phase transition, confirming universality class and estimating critical exponents.

Findings

Second-order phase transition observed

Critical exponent 1/nu=1.463(3) estimated

Anisotropy found to be irrelevant to universality class

Abstract

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.