English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the Curie-Weiss model at a given initial temperature in vanishingexternal field evolving under a Glauber spin-flip dynamics corresponding to apossibly different temperature. We study the limiting conditional probabilitiesand their continuity properties and discuss their set of points ofdiscontinuity (bad points). We provide a complete analysis of the transitionbetween Gibbsian and non-Gibbsian behavior as a function of time, extendingearlier work for the case of independent spin-flip dynamics. For initialtemperature bigger than one we prove that the time-evolved measure stays Gibbsforever, for any (possibly low) temperature of the dynamics. In the regime ofheating to low-temperatures from even lower temperatures, when the initialtemperature is smaller than the temperature of the dynamics, and smaller than1, we prove that the time-evolved measure is Gibbs initially and becomesnon-Gibbs after a sharp transition time. We find this regime is further dividedinto a region where only symmetric bad configurations exist, and a region wherethis symmetry is broken. In the regime of further cooling from low-temperaturesthere is always symmetry-breaking in the set of bad configurations. These badconfigurations are created by a new mechanism which is related to theoccurrence of periodic orbits for the vector field which describes the dynamicsof Euler-Lagrange equations for the path large deviation functional for theorder parameter. To our knowledge this is the first example of the rigorousstudy of non-Gibbsian phenomena related to cooling, albeit in a mean-fieldsetup.

Low-temperature dynamics of the Curie-Weiss Model: Periodic orbits, multiple histories, and loss of Gibbsianness