  We study zero temperature correlation functions of the spin-$1\over 2$
Heisenberg XXZ model in the critical regime $-1< \Delta\leq 1$ in a magnetic
field by means of the {\tenit Dual Field Approach}. We show for one particular
example how to derive determinant representations for correlation functions and
how to use these to embed the correlation functions in integrable systems of
integro-difference equations (IDE). These IDE are associated with a
Riemann-Hilbert problem.
