Painlevé transcendent describes quantum correlation function of the XXZ antiferromagnet away from the free-fermion point

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