Gibbs Measures for Long-Range Ising Models
Arnaud Le Ny (LAMA)
TL;DR
This paper reviews historical and recent results on one- and two-dimensional long-range Ising models, focusing on interface behavior and phase transitions, highlighting developments since the 1980s.
Contribution
It synthesizes old and new findings on interface fluctuations and states in long-range Ising models across different dimensions.
Findings
Revisits classical results from the 1980s.
Describes recent advances in interface fluctuation analysis.
Explores phase transition phenomena in low-dimensional long-range models.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods