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Gibbs–non-Gibbs properties for evolving Ising models on trees

Aernout C. D. van EnterVictor N. ErmolaevGiulio IacobelliChristof Külske — 2012

Annales de l'I.H.P. Probabilités et statistiques

In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each...

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