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arXiv · 1705.03156

Entropic repulsion and lack of the $g$-measure property for Dyson models

Rodrigo Bissacot·Eric Ossami Endo·Aernout C. D. van Enter·Arnaud Le Ny
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Abstract

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.

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Rodrigo Bissacot, Eric Ossami Endo, Aernout C. D. van Enter, Arnaud Le Ny. 2017-05-15. Entropic repulsion and lack of the $g$-measure property for Dyson models. https://doi.org/10.1007/s00220-018-3233-6

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