Correlations and Spontaneous Magnetization of the TwoDimensional Ising Model
Abstract
In this paper we rederive, by simpler methods, the OnsagerKaufman formulas for the correlations and the Onsager formula for the spontaneous magnetization of the rectangular twodimensional 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 OnsagerKaufman 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 February 1963
 DOI:
 10.1063/1.1703955
 Bibcode:
 1963JMP.....4..308M