Universality of self-organized phase transitions in driven three-dimensional magnetic systems with competing dynamics

We investigate the non-equilibrium stationary states of the Ising, XY, and Heisenberg models on a simple cubic lattice using Monte Carlo simulations. The system’s evolution is governed by a competition between two dynamics controlled by a parameter q: a one-spin flip dynamic that drives the system, in contact with a thermal reservoir at temperature T, toward a lower energy state with probability q, and a two-spin flip dynamic that drives it, subjected to an external energy flux, toward a higher energy state with probability 1−q. We construct the phase diagram of T as a function of q, which exhibits a rich phenomenology of self-organization across the different observed phases and is characterized by continuous phase transitions between them. For all three models, we identify three distinct phases: an antiferromagnetic ordered phase at low q values, a disordered paramagnetic phase at intermediate q, and a ferromagnetic ordered phase at high q values and low T. Furthermore, we calculate the critical exponents for the phase transitions and show that they remain unchanged from their equilibrium values, indicating that the non-equilibrium nature of the dynamics does not alter the universality class of the models. This suggests that the underlying symmetries of the models are the primary determinants of their critical behavior, even in the presence of a persistent energy flux.