# Gibbs Measures for Long-Range Ising Models

@article{Ny2019GibbsMF, title={Gibbs Measures for Long-Range Ising Models}, author={Arnaud Le Ny}, journal={arXiv: Mathematical Physics}, year={2019} }

This review-type paper is based on a talk given at the conference Etats de la Recherche en Mecanique 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.

## 2 Citations

### Decimations for two-dimensional Ising and rotator models

- PhysicsJournal of Mathematical Physics
- 2022

We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range as well as vector-spin interactions. Our main tools consist in a two-dimensional use of…

### Gaussian Concentration and Uniqueness of Equilibrium States in Lattice Systems

- MathematicsJournal of Statistical Physics
- 2020

We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space SZd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

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