100 years of the (critical) Ising model on the hypercubic lattice

Abstract

We take the occasion of this article to review 100 years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical mechanics. We wish, through its history, to outline some of these amazing developments. We restrict our attention to the ferromagnetic nearest-neighbor model on the hypercubic lattice, and essentially focus on what happens at or near the so-called critical point.