10-149 A.C.D. van Enter, V.N. Ermolaev, G. Iacobelli, C. Kuelske,

Gibbs-non-Gibbs properties for evolving Ising models on trees. (518K, pdf) Sep 17, 10

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Abstract. In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an in finite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero fi eld is the free-boundary-condition Gibbs state) behaves diff erently from the plus and the minus state. E.g. at large times, all confi gurations are bad for the intermediate state, whereas the plus con figuration never is bad for the plus state. Moreover, we show that for each state there are two transitions. For the intermediate state there is a transition from a Gibbsian regime to a non-Gibbsian regime where some, but not all con figurations are bad, and a second one to a regime where all confi gurations are bad. For the plus and minus state, the two transitions are from a Gibbsian regime to a non-Gibbsian one and then back to a Gibbsian regime again.

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