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

Victor Ermolaev, Christof Kuelske*

*Corresponding author for this work

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Abstract

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.

Original languageEnglish
Pages (from-to)727-756
Number of pages30
JournalJournal of Statistical Physics
Volume141
Issue number5
DOIs
Publication statusPublished - Dec-2010

Keywords

  • Gibbs measures
  • Non-Gibbsian measures
  • Non-equilibrium dynamics
  • Mean-field systems
  • Low-temperature dynamics
  • Path large deviations
  • Phase transitions
  • Periodic orbits
  • RENORMALIZATION-GROUP TRANSFORMATIONS
  • GIBBS MEASURES
  • RECOVERY
  • FIELD

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