**
Below is the ascii version of the abstract for 05-357.
The html version should be ready soon.**Christof Kuelske and Arnaud Le Ny
Spin-flip dynamics of the Curie-Weiss model: Loss of Gibbsianness with possibly broken symmetry.
(1285K, postscript)
ABSTRACT. We study the conditional probabilities of the Curie-Weiss Ising
model in vanishing external field under a symmetric independent
stochastic spin-flip dynamics and discuss their set of bad
configurations (points of discontinuity). We exhibit a complete
analysis of the transition between Gibbsian and non-Gibbsian
behavior as a function of time, extending the results for the
corresponding lattice model, where only partial answers can be
obtained.
For initial inverse temperature $\b \leq 1$, we prove that the
time-evolved measure is always Gibbsian. For $1 < \b \leq
\frac{3}{2}$, the time-evolved measure loses its Gibbsian
character at a sharp transition time. For $\b > \frac{3}{2}$, we
observe the new phenomenon of symmetry-breaking of bad
configurations: The time-evolved measure loses its Gibbsian
character at a sharp transition time, and bad configurations with
non-zero spin-average appear. These bad configurations merge into
a neutral configuration at a later transition time, while the
measure stays non-Gibbs.
In our proof we give a detailed analysis of the phase-diagram of a
Curie-Weiss random field Ising model with possibly non-symmetric
random field distribution. This analysis requires a careful study
of the minimizers of some rate-function in the framework of
bifurcation analysis.