We compute exactly the spin-spin correlation functions for the two-dimensional Ising model on a square lattice in zero magnetic field for and . We then analyze the correlation functions in the scaling limit such that is fixed. In this scaling limit , where is the scaling variable and and are the scaling functions ( is the correlation length). We derive exact expressions for these scaling functions, in terms of a Painlevé function of the third kind and analyze both the small- and large- behavior. A table of values for (good to ten significant digits) is also given. As an application we computer the coefficients and in the expansion of the zero-field susceptibility as .
- Received 13 May 1975
- Published in the issue dated 1 January 1976
© 1976 The American Physical Society