  We provide a comprehensive account of prethermal discrete time crystals
within classical Hamiltonian dynamics, complementing and extending our recent
work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting
spins on one-, two-, and three-dimensional hypercubic lattices, we investigate
the interplay between dimensionality and interaction range in the stabilization
of these non-equilibrium phases of matter that break the discrete
time-translational symmetry of a periodic drive.
