Explosive Phase Transition in a Majority-Vote Model with Inertia
  We generalize the original majority-vote model by incorporating an inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous type to a discontinuous or an explosive one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition. 
Hanshuang Chen, Chuansheng Shen, Haifeng Zhang, Guofeng Li, Zhonghuai   Hou and J\"urgen Kurths
physics.soc-ph cond-mat.stat-mech