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.
https://hal-cea.archives-ouvertes.fr/cea-01534824
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Submitted on : Thursday, June 8, 2017 - 11:47:21 AM Last modification on : Monday, February 10, 2020 - 6:13:40 PM Long-term archiving on: : Saturday, September 9, 2017 - 12:41:22 PM
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⟩