The free-fermion model in presence of fields discussed by Felderhof is reformulated as a solution of the Yang-Baxter equation associated with a family of 2-dimensional vector spaces. The trigonometric limit of this solution is equal to the Yang-Baxterization of the state model related to the multi-variable Alexander polynomial of links. This trigonometric limit is also equal to the R-matrix with respect to a family of representations of U(q)(sl2) at q = square-root -1 of affine type.