From form factors to correlation functions. The Ising model

Abstract

Abstract Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painleve III nonlinear differential equation. We also snow that the generating function of the correlation functions of the descendents of the spin and disorder operators is an N -soliton, N → ∞, τ-funtion of the sinh-Gordon hierarchy. We discuss a relation of our approach to isomonodromy deformation problems, as well as further possible generalizations.