Thermodynamic limit of the six-vertex model with reflecting end

We study the thermodynamic limit of the six-vertex model with domain wall boundary and reflecting end. We have found a number of special points where the partition function is directly obtained. We take the homogeneous limit of the Tsuchiya determinant formula of the partition function. This determinant formula satisfies the bidimensional Toda equation. We exploit this fact in order to take the thermodynamic limit and obtain the free energy of the six-vertex model with reflecting end. We successfully determined the free energy and entropy in the disordered regime.