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The roughening phase diagram of the d=3 Ising model with uniaxiallyanisotropic interactions is calculated for the entire range of anisotropy, fromdecoupled planes to the isotropic model to the solid-on-solid model, usinghard-spin mean-field theory. The phase diagram contains the line of orderingphase transitions and, at lower temperatures, the line of roughening phasetransitions, where the interface between ordered domains roughens. Uponincreasing the anisotropy, roughening transition temperatures settle after theisotropic case, whereas the ordering transition temperature increases toinfinity. The calculation is repeated for the d=2 Ising model for the fullrange of anisotropy, yielding no roughening transition.

Interface-Roughening Phase Diagram of the Three-Dimensional Ising Model for All Interaction Anisotropies from Hard-Spin Mean-Field Theory