Painlev\'e Transcendent Describes Quantum Correlation Function of the   XXZ Antiferromagnet away from the free-fermion point
  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. 
Fabian H. L. Essler, Holger Frahm, Alexander R. Its and Vladimir E.   Korepin