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Nonequilibrium lattice models: A case with effective Hamiltonian in d dimensions.

The steady-state configurational distribution of an Ising-type family of competing dynamics lattice models is explicitly found for any dimension. These models are characterized by a spin-flip dynamics which is a linear superposition of transition rates. Each individual rate attempts to drive the system asymptotically to a different equilibrium state. In general, the stationary distribution of this kind of model is not known for dimensions higher than 1. However, for a particular type of rate, we show that the stationary state is a Gibbsian one with an effective Hamiltonian whose coupling constants depend on the details of the dynamics. As an application, some related magnetic impure models are studied.