Sheared Ising models in three dimensions

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 [A. Hucht and S. Angst, EPL 100, 20003 (2012)]. 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.