The Ising model: Highlights and perspectives

TL;DR

This paper provides a non-technical overview of the Ising model, highlighting its successes and challenges in probability and mathematical physics, including phase transitions, scaling, and universality.

Contribution

It offers a concise summary of key concepts and recent developments in the study of the Ising model, emphasizing its theoretical significance and open problems.

Findings

Discussion of phase transition theory in the Ising model

Insights into scaling and renormalization group methods

Overview of universality and disordered systems

Abstract

We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase transitions, and ideas like scaling, renormalization group, universality, SLE, and random symmetry breaking in disordered systems and networks. This note is based on a talk given on 15 August 2024, as part of the Ising lecture during the 11th Bernoulli-IMS world congress, Bochum.