Ising Systems with Conflicting Dynamics: Exact Results for Random Interactions and Fields

We report on exact results for stochastic Ising systems that evolve in time due to a simultaneous action of several independent spin-flip mechanisms. The transition probability describes a competition between different values for the two parameters characterizing the involved (nearest-neighbour) Hamiltonian, namely, the interaction strength and the applied magnetic field. Such a conflicting dynamics aims to represent the sort of diffusing microscopic disorder that may occur in real systems. We determine the steady states for a class of transition probabilities for one-dimensional lattices; they exhibit amazing critical behaviour. Furthermore, it is shown that the steady state for a singular class of transition probabilities may be represented by an effective Hamiltonian that has the Ising structure with complex parameters for any lattice dimension.