Abstract
The correlation length and the free energy of the S=1/2 XXZ chain in a magnetic field in the z direction are calculated with use of a set of equations for a series of infinite numbers. These are derived by the Bethe-ansatz method for the quantum transfer matrix. The equations for free energy should be equivalent to the thermodynamic Bethe-ansatz nonlinear integral equations. A numerical method that calculates precisely the free energy and the correlation length is given.