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

##### Institute for Theoretical Physics, University Linz, Austria

The live of Ernst Ising and the steps to solving the model named after him
are reported in parallel

[1]. 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, especially for Lenz
as reflected in his approval of the thesis. It was unknown that the model
combines extraordinary simplicity with considerable complexity in the final
output including concepts of great generality.

Wolfgang Pauli who was at the same time assistant of Lenz in Hamburg
published 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 Ising
model, as he called it, in the form we know it today and reignited belief that
a 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 in
hand with damaging the network of researchers dealing with the problem
of ferromagnetism and more generally with phase transitions and statistical
physics. Such a geneological network has been identified by Elliott Montroll
as the Vienna School of Statistical Thought

[2] connecting several generations
of scientists.

In 1944 Lars Onsager presented a solution of the two-dimensional case, which
led to a first step to prove the importance of the model for understanding
critical phenomena and the liberation of Luxemburg by the American troops
rescued finally Ising’s family. In 1952 Chen-Ning Yang solved the problem of
Ising’s thesis in two dimensions; one year later Ising became US citizen. 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.

**References:**
[1] T. Ising, R. Folk, R. Kenna, B. Berche, Yu. Holovatch, The fate of Ernst Ising and the fate of his model (and reviews refered therein),

Journal of Physical Studies **21**(3), 3002 (2017) .

arXiv:physics.hist-ph/1706.01764.

[2] Elliot W. Montroll, On the Vienna School of statistical thought,

AIP Conference Proceedings **109**, 1 (1984).