 05357 Christof Kuelske and Arnaud Le Ny
 Spinflip dynamics of the CurieWeiss model: Loss of Gibbsianness with possibly broken symmetry.
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Oct 14, 05

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Abstract. We study the conditional probabilities of the CurieWeiss Ising
model in vanishing external field under a symmetric independent
stochastic spinflip dynamics and discuss their set of bad
configurations (points of discontinuity). We exhibit a complete
analysis of the transition between Gibbsian and nonGibbsian
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
timeevolved measure is always Gibbsian. For $1 < \b \leq
\frac{3}{2}$, the timeevolved measure loses its Gibbsian
character at a sharp transition time. For $\b > \frac{3}{2}$, we
observe the new phenomenon of symmetrybreaking of bad
configurations: The timeevolved measure loses its Gibbsian
character at a sharp transition time, and bad configurations with
nonzero spinaverage appear. These bad configurations merge into
a neutral configuration at a later transition time, while the
measure stays nonGibbs.
In our proof we give a detailed analysis of the phasediagram of a
CurieWeiss random field Ising model with possibly nonsymmetric
random field distribution. This analysis requires a careful study
of the minimizers of some ratefunction in the framework of
bifurcation analysis.
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