Two-temperature kinetic Ising model in one dimension: Steady-state correlations in terms of energy and energy flux

We study the nonequilibrium properties of a one-dimensional kinetic Ising model in which spins interact by nearest-neighbor ferromagnetic interactions and a spin-flip dynamics is generated by contact with heat baths that are at different temperatures on even and odd lattice sites. The average energy ({ε}) and the energy flux between the two sublattices (j_ε) are calculated exactly and the two-spin steady-state correlations are expressed through {ε} and j_ε. It is found that the correlations can be classified as ferromagnetic (for {ε}0 and j_ε small), antiferromagnetic ({ε}>0, j_ε small), oscillating ferromagnetic ({ε}0, j_ε large), and oscillating antiferromagnetic ({ε}>0, j_ε large). We also find a disorder line ({ε}=0, j_ε arbitrary) on which all correlations are zero. The character of spatial correlations is shown to be reflected in the time evolution of sublattice magnetizations: The dynamics is purely relaxational in the ferromagnetic and antiferromagnetic regime while it is damped oscillatory in the oscillating ferromagnetic and antiferromagnetic regions.