  The XXZ quantum spin chain has a triple point in its ground state
$h$-$1/\Delta$ phase diagram. This first order critical point is located at the
joint end point of the two second order phase transition lines marking the
transition from the gapless phase to the fully polarized phase and to the
N\'eel ordered phase, respectively. We explore the magnetization and the
short-range correlation functions in its vicinity using the exact solution of
the model. In the critical regime above the triple point we observe a strong
variation of all physical quantities on a low energy scale of order $1/\Delta$
induced by the transversal quantum fluctuations. We interpret this phenomenon
starting from a strong-coupling perturbation theory about the highly degenerate
ground state of the Ising chain at the triple point. From the perturbation
theory we identify the relevant scaling of the magnetic field and of the
temperature. Applying the scaling to the exact solutions we obtain explicit
formulae for the magnetization and short-range correlation functions at low
temperatures.
