Low-Temperature Dynamics of the Curie-Weiss Model: Periodic Orbits, Multiple Histories, and Loss of Gibbsianness

We consider the Curie-Weiss model at initial temperature 0 For initial temperature beta (-1)> 1 we prove that the time-evolved measure stays Gibbs forever, for any (possibly low) temperature of the dynamics. In the regime of heating to low-temperatures from even lower temperatures, 0 In the regime of further cooling from low-temperatures, beta'(-1) To our knowledge this is the first example of the rigorous study of non-Gibbsian phenomena related to cooling, albeit in a mean-field setup