The 16-dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points, i.e. points corresponding to models which possess extra symmetries not existing in nearby points. Equivalence classes of models having the same partition function are identified by means of...

The analysis of the bifurcation structure in the 16-dimensional parameter space of homogeneous (sixteen-) vertex models, started in part I, is completed in this paper. As before equivalence classes of models having the same partition function are identified by means of a 4 × 4 diagonal matrix N...

In a previous paper, the partition function of the 16-vertex model was shown to be invariant under a group of linear transformations in the space of the vertex weights. According to a theorem by Hilbert, every algebraic invariant such as the partition function for a finite lattice can be...

The end-to-end distribution function for a polymer chain with self-interaction is derived from a functional having the significance of a generator for connected diagrams which consist of vertices representing clusters of monomers in contact, and lines representing free polymer sections. In spite...

The search for bifurcation points in the parameter space of sixteen vertex models as described in three papers by Gaaff and Hijmans1) and Hijmans and Schram2,3), canbe considerably simplified and clarified by representing the equivalence classes of models having the same partition function by...

We analyse the end-to-end distribution function of a polymer chain with a pair-wise interaction between its repeat units in a continuous space. By means of a cluster expansion we classify its contributions according to the number and arrangement of the contacts between the repeat units. We then...

The construction of a complete system of basic invariants for the sixteen-vertex model on an M x N lattice as described in part I is repeated by means of an alternative method based on the theory of algebraic invariants. We use a generalization of a theorem by Cayley and Sylvester to determine...

A new analysis is made of the symmetry group of the general homogeneous 16-vertex model on a square lattice, i.e. the group of transformations in the parameter space of the model leaving invariant its partition function. The set of 16 vertex weights is decomposed in such a way that the ensuing...

We shall construct a hierarchy of subclasses of the 16-vertex model having qualitatively different symmetry properties. We determine the bifurcation points in the parameter space of the model where new symmetry elements are added to the invariance group of the partition function. In this paper...

We explore the consequences of the existence of a group of linear symmetry transformations for the sixteen-vertex model. An arbitrary sixteen-vertex model is shown tobe equivalent to a standard model, described in terms of ten parameters having an invariant significance. The general eight-vertex...