Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model

TL;DR

This paper reviews the historical development and derivation of the spontaneous magnetization formula for the square-lattice Ising model by Onsager and Kaufman, including newly available correspondence and draft calculations.

Contribution

It provides a detailed historical and technical analysis of Onsager and Kaufman's original derivation of the Ising model's spontaneous magnetization.

Findings

Reveals the development process of the Onsager-Kaufman calculation

Includes a draft paper confirming their derivation

Provides context through correspondence and historical notes

Abstract

Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C. N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman's method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.