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Critical behavior of order parameter at the nonequilibrium phase transition of the Ising model

After a quench of transverse field, the asymptotic long-time state of Ising model displays a transition from a ferromagnetic phase to a paramagnetic phase as the post-quench field strength increases, which is revealed by the vanishing of the order parameter defined as the averaged magnetization over time. We estimate the critical behavior of the magnetization at this nonequilibrium phase transition by using mean-field approximation. In the vicinity of the critical field, the magnetization vanishes as the inverse of a logarithmic function, which is significantly distinguished from the critical behavior of order parameter at the corresponding equilibrium phase transition, i.e. a power-law function.