A kinetic ANNNI model

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Abstract
We present a kinetic lattice system that evolves in general towards steady nonequilibrium states due to dynamical conflict between nearest- and next-nearest-neighbour interactions. Under two simple particular limits, the system would reach asymptotically the canonical equilibrium states for the ordinary Ising model and for the axial next-nearest-neighbour Ising (ANNNI) model, respectively. We find more generally that, independently of the lattice dimension, the steady state probability distribution for a given class of transition rates has a quasi-canonical structure with a short-range effective Hamiltonian. We solve exactly the one-dimensional version of this case, and compare its behaviour to the one for the ordinary ANNNI model. In particular, the system is shown to exhibit several spatially modulated phases and impure critical points. We also obtain some information on the phase diagram for the two-dimensional lattice.