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.