On the classification of the homogeneous 16-vertex models on a square lattice

In the previous paper we have shown that the classification problem of the homogeneous real 16-vertex models on a square lattice as proposed by Gaaff and Hijmans is closely connected with the similar problem corresponding to the boson Bogoliubov transformation in quantum mechanics. This insight leads us in the present paper to use arguments and examples from papers dealing with the latter problem in a further study of the classification problem of the real 16-vertex models. We also use a somewhat modified concept of “standard (or normal) 16-vertex model” which was introduced by Hijmans and Schram in a similar study concerning the complex 16-vertex models. We show that, rather than the single family found by Hijmans and Schram for the complex variant of the problem, the set of equivalence classes of real 16-vertex models can be divided up into seven families. This strongly suggests the existence of a new type of phase transitions which manifest themselves when the physical system in the 16-parameter space “moves” from one family to another.