On general-n coefficients in series expansions for row spin–spin correlation functions in the two-dimensional Ising model

Abstract

Abstract We consider spin–spin correlation functions for spins along a row, R n = ⟨σ 0,0 σ 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 a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨σ 0,0 σ n,n ⟩ in this model.