One-dimensional kinetic Ising model with competing dynamics: Steady-state correlations and relaxation times

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Abstract
A one-dimensional kinetic Ising model with dynamics characterized by a combination of spins flips at temperature T and spin exchanges at T=∞ is studied. The two-spin correlations in the steady state are calculated exactly and the decay times describing the relaxation of both the magnetization and the two-spin correlations are also given. We find that neither the steady-state nor the dynamic quantities show any sign of a phase transition that could exist in this one-dimensional, nonequilibrium system. Two remarkable features of the solution are that (i) the correlation length in the steady state with random spin exchanges is larger than the correlation length in the corresponding equilibrium state without spin exchanges, and (ii) a fluctuation-dissipation theorem is satisfied in the nonequilibrium steady state.