THE SURVIVAL OF ERNST ISING AND THE STRUGGLE TO SOLVE HIS MODEL

Reinhard Folk (Personal webpage)

The live of Ernst Ising and the steps to solving the model named after himare reported in parallel [1]. Wilhelm Lenz suggested his student Ernst Isingto explain the existence of ferromagnetism on the basis of his publication in1920. The result, published in 1925 was disappointing, especially for Lenzas reflected in his approval of the thesis. It was unknown that the modelcombines extraordinary simplicity with considerable complexity in the finaloutput including concepts of great generality.

Wolfgang Pauli who was at the same time assistant of Lenz in Hamburgpublished in the same year his ‘nichtklassische Zweideutigkeit ...’, 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 Isingmodel, as he called it, in the form we know it today and reignited belief thata ferromagnetic phase transition might be possible in this model.Meanwhile Ising had left university research and due to the political situation in 1938 had to leave Germany and fled to Luxemburg. This went inhand with damaging the network of researchers dealing with the problemof ferromagnetism and more generally with phase transitions and statisticalphysics. Such a geneological network has been identified by Elliott Montrollas the Vienna School of Statistical Thought [2] connecting several generationsof scientists.

In 1944 Lars Onsager presented a solution of the two-dimensional case, whichled to a first step to prove the importance of the model for understandingcritical phenomena and the liberation of Luxemburg by the American troopsrescued finally Ising’s family. In 1952 Chen-Ning Yang solved the problem ofIsing’s thesis in two dimensions; one year later Ising became US citizen. Thefollowing development showed, that the model turned out to be a highwayto modern physics concepts applicable also in other fields, although the finalexact solution in three dimensions has not yet been reached.