van Enter, A. C. D.; Fernández, R.; den Hollander, F.; Redig, F. Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures. (English) Zbl 0990.82018 Commun. Math. Phys. 226, No. 1, 101-130 (2002). Summary: We consider Ising-spin systems starting from an initial Gibbs measure \(\nu\) and evolving under a spin-flip dynamics towards a reversible Gibbs measure \(\mu\neq\nu\). Both \(\nu\) and \(\mu\) are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure \(\nu S(t)\) at time \(t\) and show the following:(1) For all \(\nu\) and \(\mu\), \(\nu S(t)\) is Gibbs for small \(t\).(2) If both \(\nu\) and \(\mu\) have a high or infinite temperature, then \(\nu S(t)\) is Gibbs for all \(t>0\).(3) If \(\nu\) has a low non-zero temperature and a zero magnetic field and \(\mu\) has a high or infinite temperature, then \(\nu S(t)\) is Gibbs for small \(t\) and non-Gibbs for large \(t\).(4) If \(\nu\) has a low non-zero temperature and a non-zero magnetic field and \(\mu\) has a high or infinite temperature, then \(\nu S(t)\) is Gibbs for small \(t\), non-Gibbs for intermediate \(t\), and Gibbs for large \(t\).The regime where \(\mu\) has a low or zero temperature and \(t\) is not small remains open. This regime presumably allows for many different scenarios. Cited in 3 ReviewsCited in 38 Documents MSC: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:stochastic evolution; Ising-spin systems; Gibbs measure; spin-flip dynamics PDFBibTeX XMLCite \textit{A. C. D. van Enter} et al., Commun. Math. Phys. 226, No. 1, 101--130 (2002; Zbl 0990.82018) Full Text: DOI arXiv