Gibbs Measures for Long-Range Ising Models

Arnaud Le Ny (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

This review-type paper is based on a talk given at the conference États de la Recherche en Mécanique statistique, which took place at IHP in Paris (December 10-14, 2018). We revisit old results from the 80's about one dimensional long-range polynomially decaying Ising models (often called Dyson models in dimension one) and describe more recent results about interface fluctuations and interface states in dimensions one and two.

Mots clés: Phase coexistence; Long-range Ising models; Non-Gibbsian measures; Interface states; Renormalization; Gibbs vs. g-measures

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Arnaud Le Ny. Gibbs Measures for Long-Range Ising Models. 2019. ⟨hal-02343596⟩