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 (ɛ) and the energy flux between the two sublattices (${\mathit{j}}_{\mathrm{\varepsilon }}$) are calculated exactly and the two-spin steady-state correlations are expressed through ɛ and ${\mathit{j}}_{\mathrm{\varepsilon }}$. It is found that the correlations can be classified as ferromagnetic (for ɛ0, ${\mathit{j}}_{\mathrm{\varepsilon }}$ small), oscillating ferromagnetic (ɛ0, ${\mathit{j}}_{\mathrm{\varepsilon }}$ large). We also find a disorder line (ɛ=0, ${\mathit{j}}_{\mathrm{\varepsilon }}$ 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.