  We consider the Ferromagnetic-String-Formation-Probability correlation
function (FSFP) for the spin-$1\over 2$ Heisenberg XXZ chain. We construct a
completely integrable system of integro-difference equations (IDE), which has
the FSFP as a $\tau$-function. We derive the associated Riemann-Hilbert problem
and obtain the large distance asymptotics of the FSFP correlator in some
limiting cases.
