Functions Characterizing the Ground State of the XXZ Spin-1/2 Chain in the Thermodynamic Limit

We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-$1/2$ chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed energy, dressed charge and density of Bethe roots. Furthermore, we establish that given a fixed external magnetic field (or a fixed magnetization) there exists a unique value of the boundary of the Fermi zone.