By employing Monte Carlo simulations, we investigate the isotropic Heisenberg system model on a simple cubic lattice with short-range interactions, allowing the system to evolve toward a steady state under the influence of competition between Glauber and Kawasaki dynamics. With probability $q$, the system is in contact with a thermal reservoir at temperature $T$ and evolves toward the lower energy state through Glauber dynamics. However, with probability $1-q$, the system is subjected to an external energy flux that drives it toward the higher energy state through Kawasaki dynamics. By analyzing the phase diagram of $T$ versus $q$, our findings show: (i) second-order phase transitions at high $q$ and intermediate $T$ values and first-order phase transitions below the tricritical point at $(q_t,T_t)=(0.615\pm 0.004,0.905\pm 0.001)$, and (ii) the phenomenon of unstable self-organization in the system in which the antiferromagnetic phase is only found at $q=0$ with an initial antiferromagnetic state; however, as $q$ increases at low temperatures, the system evolves to the ordered ferromagnetic phase.

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• Magnetic order
• Phase diagrams
• Classical spin models
• Heisenberg model
• Monte Carlo methods