Gibbs Measures for Long-Range Ising Models

This review-type paper is based on a talk given at the conference {'E}tats de la Recherche en M{'e}canique 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.