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 0For 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, 0In 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.