Modified rational six vertex model on a rectangular lattice: New formula, homogeneous and thermodynamic limits

We continue the work of [S. Belliardet al., SciPost Phys. 16, 009 (2024)] studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified Izergin one and a Vandermonde one. This expression enables us to compute the partition function in the homogeneous limit for the rectangular lattice, and then to study the thermodynamic limit. It leads to a new result, we obtain the first order of free energy with boundary effects in the thermodynamic limit.