Schottky’s forgotten step to the Ising model

Reinhard Folk, Yurij Holovatch

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A longstanding problem in natural science and later in physics was the understanding of the existence of ferromagnetism and its disappearance under heating to high temperatures. Although a qualitative description was possible by the Curie–Weiss theory, it was obvious that a microscopic model was necessary to explain the tendency of the elementary magnetons to prefer parallel ordering at low temperatures. Such a model was proposed in 1922 by Schottky within the old Bohr–Sommerfeld quantum mechanics and claimed to explain the high values of the Curie temperatures of certain ferromagnets. Based on this idea Ising formulated a new model for ferromagnetism in solids. Simultaneously the old quantum mechanics was replaced by new concepts of Heisenberg and Schrödinger and the discovery of spin. Thus Schottky’s idea was outperformed and finally replaced in 1928 by Heisenberg exchange interaction. This led to a reformulation of Ising’s model by Pauli at the Solvay conference in 1930. Nevertheless one might consider Schottky’s idea as a forerunner of this development explaining and asserting that the main point is the Coulomb energy leading to the essential interaction of neighboring elementary magnets.

Original languageEnglish
Article number9
Number of pages18
JournalEuropean Physical Journal H
Issue number1
Publication statusPublished - 6 Sept 2022

Bibliographical note

This is an open access article distributed under the terms of the Creative Commons CC BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


R.F. thanks Sigismund Kobe for discussions on the Schottky anomaly. The authors are thankful to Bertrand Berche and Ralph Kenna for a longstanding collaboration on a history of Ising model and for reading and discussing this paper prior to publication. We also highly acknowledge the support by the Austrian Agency for International Cooperation in Education and Research (OeAD) and the Ministry of Education and Science of Ukraine via bilateral Austro-Ukrainian grant number UA 09/2020. Yu.H. acknowledges support of the JESH mobility program of the Austrian Academy of Sciences and hospitality of the Complexity Science Hub Vienna when finalizing this paper.

Publisher Copyright:
© 2022, The Author(s).

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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