  We consider a dissipative quantum Ising model periodically driven by a train
of $\pi$-pulses and investigate dissipative discrete time crystals (DTCs) in
solids. In this model, the interaction between the spins spontaneously breaks
the discrete time translation symmetry, giving rise to a dissipative DTC, where
two ferromagnetic states are switched alternately by each pulse. We
microscopically describe the generic dissipation due to thermal contact to an
equilibrium heat bath using the Bloch-Redfield equation. In contrast to other
DTC studies, this dissipation stabilizes, rather than destroys, the DTC order
without fine-tuning as long as the temperature is low enough. Invoking the
time-dependent mean-field theory and solving self-consistently the periodic
drive, dissipation, and DTC order parameter, we investigate the nonequilibrium
DTC phase transition and determine the critical exponents, including a
dynamical one. We also find phase transitions without equilibrium counterpart:
a nontrivial interplay of the periodic drive and dissipation gives rise to
reentrant DTC transition when changing the pulse interval at a fixed
temperature. Besides, to demonstrate the rigidity of the DTC, we consider
imperfect $\pi$-pulses, showing that the DTC is robust against the small
imperfections and finding that discrete time quasicrystals (DTQC) can appear
for the larger imperfections. Together with experimental proposals in magnetic
materials, our results pave the ways for realizing the DTC and for uncovering
nonequilibrium critical phenomena in real solid-state materials.
