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Spin-flip dynamics of the Curie-Weiss model: loss of Gibbsianness with possibly broken symmetry. (English) Zbl 1138.82012

The authors study the conditional probabilities of the Curie-Weiss Ising model in a vanishing external field under a symmetric independent stochastic spin-flip dynamics and discuss their set of points of discontinuity.
The main result is following: i) for an initial temperature \(\beta ^{-1}\geq1\) the time-evolved measure is always Gibbsian; ii) for \(\frac{2}{3}\leq \beta ^{-1}<1\), the time-evolved measure loses its Gibbsian character at a sharp transition time; iii) for \(\beta ^{-1}<\frac{2}{3}\) the new phenomenon of symmetry-breaking in the set of points of discontinuity is observed and these points corresponding to a non-zero spin-average appear a sharp transition time and give rise to biased non-Gibbsianness of the time-evolved measure.

MSC:

82B26 Phase transitions (general) in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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