Editing Lars Onsager (section)

=== Exact solution of the 2D Ising model ===
To solve the 2D Ising model, Onsager began by diagonalizing increasingly large transfer matrices. He said that it's because he had a lot of time during WWII. He began by computing the 2&nbsp;×&nbsp;2 transfer matrix of the 1D Ising model, which is already solved by Ising himself. He then computed the transfer matrix of the "Ising ladder", meaning two 1D Ising models side-by-side, connected by links. The transfer matrix is then 4&nbsp;×&nbsp;4. He repeated this for up to six 1D Ising models, resulting in transfer matrices of up to 64&nbsp;×&nbsp;64. He diagonalized all of them and found that all the eigenvalues were of a special form, so he guessed that the algebra of the problem was an [[associative algebra]] (later called the Onsager algebra<ref>{{Cite journal |last=Davies |first=B. |date=June 1990 |title=Onsager's algebra and superintegrability |url=https://dx.doi.org/10.1088/0305-4470/23/12/010 |journal=Journal of Physics A: Mathematical and General |language=en |volume=23 |issue=12 |pages=2245–2261 |doi=10.1088/0305-4470/23/12/010 |bibcode=1990JPhA...23.2245D |issn=0305-4470}}</ref>).<ref>[[Chen-Ning Yang]], ''Selected papers (1945–1980) of Chen Ning Yang With Commentary'', World Scientific Series in 20th Century Physics: Volume 36 (2005), paper and commentary [52a]. pp. 11-13</ref>

The solution involved generalized quaternion algebra and the theory of elliptic functions, which he learned from ''A Course of Modern Analysis''.<ref name=":1" />