We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.
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. \ifmmode\pm\else\textpm\fi{}
J0, symmetric bonds competing with broken ones, \ifmmode\pm\else\textpm\fi{}
J0 and J=0, nonsymmetric bonds, \ensuremath{\Vert}
J1\ensuremath{\Vert} and -\ensuremath{\Vert}
J2\ensuremath{\Vert}, 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\ensuremath{\le}3. A comparison is made with existing exact results for d=1, h=0, and \ifmmode\pm\else\textpm\fi{}
J0.
In this article, spin systems with competing interactions in an external magnetic field are investigated. The Ising model with ferromagnetic short-range forces and long-range antiferromagnetic forces is considered. Long-range forces decrease according to the power law. Long-range interaction is characterized by the rate of decrease with distance and relative intensity. The Metropolis algorithm is used for computer modeling. Two order parameters for ferromagnetic and antiferromagnetic ordering are used. The theory of finite size scaling is used. The transition temperature was defined based on Binder's cumulants for each of the order parameters. The phase diagram for the system is constructed at various values of the long-range interaction parameters. As the temperature decreases, the system can transfer from the paramagnetic phase into the ferromagnetic and antiferromagnetic ones. The type of the low-temperature phase depends on the intensity of long-range forces and does not depend on the rate of decrease of the interaction with distance. There is a boundary value of the intensity of long-range forces, below which the ferromagnetic phase is implemented, and above it is the antiferromagnetic phase. The change in the phase diagram under the influence of an external magnetic field is investigated. In an external magnetic field, the ferromagnetic phase transition becomes spread. The temperature of the antiferromagnetic phase transition in an external field decreases according to the square law. The boundary value of the intensity of long-range forces linearly grows with increasing the intensity of the external magnetic field. An increase in the boundary value in a magnetic field leads to a change in the type of the low-temperature phase. This effect is shown as a phase transition from the antiferromagnetic to the ferromagnetic phase in the external magnetic field. A comparison with the data of real experiments is carried out.