  We consider quantum correlation functions of the antiferromagnetic
spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that
for a magnetic field close to the critical field $h_c$ (for the critical
magnetic field the ground state is ferromagnetic) certain correlation functions
can be expressed in terms of the solution of the Painlev\'e V transcendent.
This establishes a relation between solutions of Painlev\'e differential
equations and quantum correlation functions in models of {\sl interacting}
fermions. Painlev\'e transcendents were known to describe correlation functions
in models with free fermionic spectra.
