Prethermalization and persistent order in the absence of a thermal phase transition

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($\ensuremath{\propto}1/{r}^{\ensuremath{\alpha}}$ with distance $r$), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of $\ensuremath{\alpha}$ for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on $\ensuremath{\alpha}$ as well as on the quench parameters.