A comment on free-fermion conditions for lattice models in two and more   dimensions
  We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions. 
J.M. Maillard and C.M. Viallet