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-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 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.