Changing the order of a dynamical phase transition through fluctuations in a quantum p-spin model

We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.