@article{3064399,
    title = "Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line",
    author = "Papakonstantinou, T. and Malakis, A.",
    journal = "Physical Review E: Statistical, Nonlinear, and Soft Matter Physics",
    year = "2013",
    volume = "87",
    number = "1",
    issn = "1539-3755, 1550-2376",
    doi = "10.1103/PhysRevE.87.012132",
    keywords = "Antiferromagnetic bonds;  Bond randomness;  Collapse analysis;  Critical behavior;  Critical exponent;  Ferromagnetic exchange;  Ferromagnetic-paramagnetic phase transition;  Ferromagnetic-paramagnetic transitions;  Logarithmic derivatives;  Magnetization data;  Numerical data;  Order parameter;  Parallel tempering;  Second orders;  Simple-cubic lattices;  Three-dimensional Ising model;  Universality class;  Z-directions, Anisotropy;  Ising model;  Paramagnetism;  Phase diagrams;  Random processes;  Three dimensional computer graphics, Three dimensional, anisotropy;  article;  computer simulation;  magnetic field;  statistical model, Anisotropy;  Computer Simulation;  Magnetic Fields;  Models, Statistical",
    abstract = "We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on 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 (pz=0;p xy=0.176). The numerical data clearly point out 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/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy. © 2013 American Physical Society."
}