Anomalous Dynamical Phase Transitions of the Ising Model Studied by the Nonequilibrium Ensemble Method: Freezing-by-Heating and Permanent Liquid.

We investigate the nonequilibrium, dynamical phase transition behavior of the one-dimensional Ising model, using the trajectory ensemble approach in the context of the large deviation theory. We introduce a double-biased ensemble, named the , -ensemble, based on nonequilibrium steady-state trajectories. The ensemble invokes the time-integrated, trajectory energy as an order parameter, coupled to its conjugate -field in addition to the dynamical activity and its conjugate field in the trajectory space. Using the dynamical free energy obtained from the large deviation formalism, we explore the rich behaviors of the dynamical phase transition of the 1D Ising model in the (, , ) parameter space, with being temperature. Among other features, we discover that novel, anomalous dynamical phase transitions are possible due to the decoupling between the dynamical activity and trajectory energy under specific conditions. In particular, we observe that the system exhibits a freezing-by-heating phenomenon as the dynamical activity decreases with temperature under a specific condition. We also find a permanent liquid phase when the equilibrium temperature and the nonequilibrium -field are exactly balanced against each other. Our results provide a useful tool for exploring the dynamical phase transition phenomena to be investigated in various systems.