Schottky’s forgotten step to the Ising model

Abstract

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.