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Entropic Repulsion and Lack of the g-Measure Property for Dyson Models

Bissacot, R., Endo, E. O., van Enter, A. C. D. & Le Ny, A., Nov-2018, In : Communications in Mathematical Physics. 363, 3, p. 767-788 22 p.

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  • Entropic Repulsion and Lack of the g-Measure Property for Dyson Models

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  • Rodrigo Bissacot
  • Eric O. Endo
  • Aernout C. D. van Enter
  • Arnaud Le Ny

We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not g-measures. The main ingredient in the proof is the occurrence of an entropic repulsion effect, which follows from the mesoscopic stability of a (single-point) interface for these long-range models in the phase transition region.

Original languageEnglish
Pages (from-to)767-788
Number of pages22
JournalCommunications in Mathematical Physics
Volume363
Issue number3
Publication statusPublished - Nov-2018

    Keywords

  • DIMENSIONAL ISING-MODEL, LONG-RANGE INTERACTIONS, GLOBAL MARKOV PROPERTY, COMPLETE CONNECTIONS, PHASE-TRANSITION, RUELLE OPERATOR, LATTICE MODELS, GENERAL-THEORY, GIBBS MEASURES, POTTS MODELS

ID: 77089714