05-357 Christof Kuelske and Arnaud Le Ny
Spin-flip dynamics of the Curie-Weiss model: Loss of Gibbsianness with possibly broken symmetry. (1285K, postscript) Oct 14, 05
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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.

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