Rates for irreversible Gibbsian Ising models

Abstract : Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of rates yielding such a stationary state for models with single-spin flip dynamics. We add some supplementary material to this study and confirm that Gibbsian irreversible Ising models exist for one and two-dimensional lattices but not for the three-dimensional cubic lattice. We also analyze asymmetric Gibbsian dynamics in the limit of infinite temperature. We finally revisit the case of a linear chain of spins under asymmetric conserved dynamics.
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Claude Godrèche. Rates for irreversible Gibbsian Ising models. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2013, 2013, pp.P05011. ⟨10.1088/1742-5468/2013/05/P05011⟩. ⟨cea-01534824⟩

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