Classical physics cannot account for ferromagnetism

[PhysicsProf]

A fascinating aspect of ferromagnetism:  it cannot be explained with classical physics!

For those looking for an "everyday object" that can only be explained via quantum mechanics - pick up a simple magnet.

The Bohr–van Leeuwen theorem is a theorem in the field of statistical mechanics. The theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero.[1] This makes magnetism in solids solely a quantum mechanical effect and means that classical physics cannot account for diamagnetism, paramagnetism or ferromagnetism.[2]
Contents  [hide]
1 History
2 Proof
2.1 An intuitive proof
2.2 A more formal proof
3 Applications of the Bohr–van Leeuwen theorem
4 See also
5 Notes
6 References
7 External links
History [edit]

What is today known as the Bohr–van Leeuwen theorem was discovered by Niels Bohr in 1911 in his doctoral dissertation[3] and was later rediscovered by Hendrika Johanna van Leeuwen in her doctoral thesis in 1919.[4] In 1932, van Vleck formalized and expanded upon Bohr's initial theorem in a book he wrote on electric and magnetic susceptibilities.[5] The significance of this discovery is that classical physics does not allow for such things as paramagnetism, diamagnetism and ferromagnetism and thus quantum physics and relativity are needed to explain the magnetic events.[2] This result, "perhaps the most deflationary publication of all time,"[6] may have contributed to Bohr's development of a quasi-classical theory of the hydrogen atom in 1913.

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[Wikipedia]

[Paul-R]

I have always thought that the domain theory is complete nonsense.
What is a domain?
How big is it?
Why not subdivide it?