Mean-field solution of a nonequilibrium random-exchange Ising-model system

We report first-order mean-field results for nonequilibrium random-exchange lattice systems, namely, Ising-like models whose kinetics involve a simultaneous, random competition between ferromagnetic and antiferromagnetic interactions that generally induces nonequilibrium steady states. We consider the competition between symmetric bonds. ±${\mathit{J}}_0$, symmetric bonds competing with broken ones, ±${\mathit{J}}_0$ and J=0, nonsymmetric bonds, ‖${\mathit{J}}_1$‖ and -‖${\mathit{J}}_2$‖, and some of those systems under an external magnetic field h. The time evolution and steady-state properties, including phase diagrams, are obtained for several lattice coordination numbers, e.g., the case of simple-cubic lattices of dimension d≤3. A comparison is made with existing exact results for d=1, h=0, and ±${\mathit{J}}_0$.