On the zero-temperature limit of gibbs states

Jean René Chazottes, Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We exhibit Lipschitz (and hence Hölder) potentials on the full shift {0,1}N such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on the configuration space {0,1}Z for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space {0,1}Zd, d ≥ 3, we show that this non-convergence behavior can occur for the equilibrium states of finite-range interactions, that is, for locally constant potentials.

Original languageAmerican English
Pages (from-to)265-281
Number of pages17
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Jul 2010
Externally publishedYes


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