The XX and Ising Limits in Integral Formulas for Finite-Temperature Correlation Functions of the XXZ Chain

We consider a multiple-integral representation for a one-parameter generating function of the finite temperature S^z-S^z correlation functions of the antiferromagnetic spin-1/2 XXZ chain in the XX limit and in the Ising limit. We show how the multiple integrals reduce to single integrals in these limits, thus reproducing known results. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 146–160, January, 2006.