Higher-order correlation functions of the planar ising model

Abstract

A method of calculating the asymptotic behaviour of the higher-order correlation functions for large distances is proposed for the planar Ising model in the absence of a magnetic field. The three-point correlation functions composed of a spin operator or of energy-density operators are considered. The asymptotic behaviour of the correlation functions for distances R ⪢ R c (where R c is the correlation radius) is determined. It is shown that the asymptotic behaviour of the correlation functions for large distances does not depend on the choice of operators. The asymptotic behaviour of the correlation functions in which two operators are relatively close to one another is considered near the critical point. The results which we obtained are compared with the predictions of the scaling laws and operator algebra.