Correlations and Spontaneous Magnetization of the Two-Dimensional Ising Model

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Abstract
In this paper we rederive, by simpler methods, the Onsager‐Kaufman formulas for the correlations and the Onsager formula for the spontaneous magnetization of the rectangular two‐dimensional Ising lattice. The Pfaffian approach is used to derive the correlations in terms of Pfaffians, and for the correlations in a row a single Toeplitz determinant is obtained which is proved equivalent to the Onsager‐Kaufman result. The spontaneous magnetization is obtained as the limiting value of an infinite Toeplitz determinant and its evaluation is facilitated by use of the generalization of a result first published by Szego.
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