Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of the and for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t -> infinite and n -> infinite with 0 <= n/t < 1,1 < n/t, or t = n + n sup(1/3)(z/2) where z is fixed of order one. In this latter region the general Painleve V solution is shown to reduce to a Painleve II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values. (orig.)