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 (alpha 1/r(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 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 alpha as well as on the quench parameters.