The Survival of Ernst Ising and the Struggle to Solve His Model

TL;DR

This paper narrates the historical development of the Ising model, highlighting key figures, political challenges, and milestones in solving the model in one and two dimensions, and its significance in modern physics.

Contribution

It provides a comprehensive historical account of the Ising model's development, including the personal and political factors influencing its study and the progression of solutions.

Findings

Ising's 1D model proved only the absence of ferromagnetism.

Onsager solved the 2D Ising model in 1944.

The 3D Ising model remains unsolved.

Abstract

The life of Ernst Ising and the steps to solving the model named after him are reported in parallel. Wilhelm Lenz suggested his student Ernst Ising to explain the existence of ferromagnetism on the basis of his publication in 1920. The result, published in 1925 was disappointing, because only the one dimensional case could be solved with a negative result about the absence of ferromagnetism. Wolfgang Pauli who was an assistant of Lenz in Hamburg published in the same year his 'nonclassical ambiguity', later identified as the spin of the electron, and the exclusion principle. He was the first - at the Solvay Conference in 1930 - to present the Hamiltonian of the Ising model as we know it today. Meanwhile Ising had left university research and due to the political situation in 1938 had to leave Germany and fled to Luxemburg. This went in hand with damaging the network of researchers dealing with the problem of ferromagnetism and more generally with phase transitions and statistical physics. In 1944, the year when Luxemburg was liberated by the American troops and Ising and his family was rescued, Lars Onsager presented a solution of the two-dimensional case. In 1952 Chen-Ning Yang solved the problem of Ising's thesis in two dimensions; one year later Ising became the US citizenship. The following development showed, that the model turned out to be a highway to modern physics concepts applicable also in other fields, although the final exact solution in three dimensions has not yet been reached.