# Origins of the Ising model

## TL;DR

This paper reviews the historical development of the Ising model from its inception in 1925 through its key theoretical validation in 1936, highlighting how simple two-state interactions lead to long-range order.

## Contribution

It provides a detailed analysis of the origins and early theoretical understanding of the Ising model up to 1936, emphasizing its foundational significance.

## Key findings

- Ising's 1925 analysis of a one-dimensional chain shows no ferromagnetic order.
- Peierls' 1936 demonstration confirms the existence of ordered states in two dimensions.
- The model's simplicity with two states and short-range interactions explains its long-term success.

## Abstract

In 1925, Ernest Ising published a paper analyzing a model proposed in 1920 by Wilhelm Lenz for ferromagnetism. The model is composed of constituent units that take only two states and interact only when they are neighbors. Ising showed that in a linear chain the model does not present an ordered ferromagnetic state, a frustrating but correct result. However, Rudolf Peierls demonstrated in 1936 that the model does in fact present an ordered state in two dimensions, and therefore in three dimensions. This result reveals that short-range interaction and only two states for each constituent unit are sufficient for ordering to occur over long distances. These two elements are the key to understanding the success of the model and its variants even a hundred years after its appearance. Here we analyze the emergence of the model in the period up to 1936.