On General-n Coefficients in Series Expansions for Row Spin-Spin Correlation Functions in the Two-Dimensional Ising Model

Abstract

We consider spin-spin correlation functions for spins along a row, $R_n=⟨{\sigma }_{0,0}{\sigma }_{n,0}⟩$, in the two-dimensional Ising model. We discuss a method for calculating general-$n$ expressions for coefficients in high-temperature and low-temperature series expansions of $R_n$ and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for an ordinary differential equation whose solution would determine $R_n$, analogous to the known ordinary differential equation whose solution determines the diagonal correlation function $⟨{\sigma }_{0,0}{\sigma }_{n,n}⟩$ in this model.

No change in original results; by request of a referee, the paper was expanded to include transcriptions of results in terms of equivalent elliptic modulus variables

References in corpus (4)

• Globally nilpotent differential operators and the square Ising model
• Fuchs versus Painlevé
• The Ising correlation $C(M,N)$ for $\nu =-k$
• On the low temperature series expansion for the diagonal correlation functions in the two-dimensional Ising model