Meta-stable states in the Ising model with Glauber-Kawasaki competing dynamics

Meta-stable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a power-law of the form, $P(k)\sim k^{-\alpha}$. The evolution towards the stationary state occurred through the competition between two dynamics, driving the system out of equilibrium. In this competition, with probability $q$, the system was simulated in contact with a heat bath at temperature $T$ by the Glauber dynamics, while with probability $1-q$, the system experienced an external energy influx governed by the Kawasaki dynamics. The phase diagrams of $T$ versus $q$ were obtained, which are dependent on the initial state of the system, and exhibit first- and second-order phase transitions. In all diagrams, for intermediate values of $T$, the phenomenon of self-organization between the ordered phases was observed. In the regions of second-order phase transitions, we have verified the universality class of the system through the critical exponents of the order parameter $\beta$, susceptibility $\gamma$, and correlation length $\nu$. Furthermore, in the regions of first-order phase transitions, we have demonstrated the instability due to transitions between the ordered phases through hysteresis-like curves of the order parameter, in addition to the existence of absorbing states. We also estimated the value of the tricritical points when the discontinuity in the order parameter in the phase transitions was no longer observed.