Spontaneous Magnetization in the Two-Dimensional Ising Model

B. N. Valuev

Vardan Apinyan

Keh-Ying Lin

Chongming Yang

The spontaneous magnetization of a two-dimensional Ising model is calculated exactly. The result also gives the long-range order in the lattice.Received 18 September 1951DOI:https://doi.org/10.1103/PhysRev.85.808©1952 American Physical Society

Elliott W. Montroll, Renfrey B. Potts, John Ward

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.

Ken‐Yu Lin, Y. G. Liu