 01200 A.C.D. van Enter, R. Fern\'andez, F. den Hollander, F. Redig
 Possible loss and recovery of Gibbsianness during the stochastic evolution
of Gibbs measures
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May 30, 01

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Abstract. We consider Isingspin systems starting from an initial Gibbs measure
$\nu$ and evolving under a spinflip dynamics towards a reversible Gibbs
measure $\mu neq \nu$. Both $\mu$ and $\nu$ are assumed to have
a finiterange 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 $t \geq 0$.
(3) If \nu$ has a low nonzero temperature and a zero magnetic field
and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs
for small t and nonGibbs for large t.
(4) If $\nu$ has a low nonzero temperature and a nonzero magnetic field
and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs
for small t, nonGibbs 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.
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