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The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures T_c which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent theta=2 as well as the correlation length exponents nu_parallel=1 and nu_perp=1/2. These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior.
We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and effective-med
Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. W
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