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.
CITATION STYLE
Bissacot, R., Endo, E. O., van Enter, A. C. D., & Le Ny, A. (2018). Entropic Repulsion and Lack of the g-Measure Property for Dyson Models. Communications in Mathematical Physics, 363(3), 767–788. https://doi.org/10.1007/s00220-018-3233-6
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