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

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.

32 pages, including copies of a draft paper almost certainly by Onsager and Kaufman Minor additions and corrections in second version

References in corpus (2)

• Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ
• Proof of the determinantal form of the spontaneous magnetization of the superintegrable chiral Potts model

Cited by in corpus (12)

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• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model: II
• Extreme boundary conditions and random tilings
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Frustrations on decorated planar lattices in Ising model
• Spontaneous magnetization of Kagome lattice in Ising model
• Leading corrections to the scaling function on the diagonal for the two-dimensional Ising model
• On the diagonal susceptibility of the 2D Ising model
• Frustrations on decorated triangular lattice in Ising model
• Frustrations on Decorated Square Lattice in Ising Model
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model
• Approximate thermodynamics of the two-dimensional Ising model in an external magnetic field