Rotational Invariance of the 2d Spin – Spin Correlation Function

Abstract

At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3–5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22–26, 1984, JINR, vol II, pp 138–151, 1985).