  Systems subject to a high-frequency drive can spend an exponentially long
time in a prethermal regime, in which novel phases of matter with no
equilibrium counterpart can be realized. Due to the notorious computational
challenges of quantum many-body systems, numerical investigations in this
direction have remained limited to one spatial dimension, in which long-range
interactions have been proven a necessity. Here, we show that prethermal
non-equilibrium phases of matter are not restricted to the quantum domain.
Studying the Hamiltonian dynamics of a large three-dimensional lattice of
classical spins, we provide the first numerical proof of prethermal phases of
matter in a system with short-range interactions. Concretely, we find
higher-order as well as fractional discrete time crystals breaking the
time-translational symmetry of the drive with unexpectedly large integer as
well as fractional periods. Our work paves the way towards the exploration of
novel prethermal phenomena by means of classical Hamiltonian dynamics with
virtually no limitations on the system's geometry or size, and thus with direct
implications for experiments.
